# Thread: solving equations

1. ## solving equations

I have worked on my math for 8 hours straight.. my brain has melted but I learned a lot today. I have 2 problems left and can not seem to get them... Can anyone show me how to work them out?

1) solve the quadratic equation...

4xsquared=13x +12

and the other is...
2) Factor Completly

9x squared+12xy+4y squared-25

I dont have long to turn this in so it is kind of urgent.. any help is GREATLY appreciated.. Thanks so much.. Heather

2. 1) $\displaystyle 4x^2=13x+12\Leftrightarrow 4x^2-13x-12=0$
$\displaystyle a=4, \ b=-13, \ c=-12$
$\displaystyle \Delta=b^2-4ac=361=19^2$
$\displaystyle x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a}$
Find $\displaystyle x_1, \ x_2$

2) $\displaystyle 9x^2+12xy+4y^2-25=(3x+2y)^2-5^2$
Now, use the identity $\displaystyle a^2-b^2=(a-b)(a+b)$

3. I dont have a clue what the first problem means or what the answer is.. it looks very confusing..

4. If you don't know the formulas for the quadratic equation, let's try to factorise the equation:
$\displaystyle 4x^2-13x-12=0\Leftrightarrow 4x^2-16x+3x-12=0\Leftrightarrow$
$\displaystyle \Leftrightarrow 4x(x-4)+3(x-4)=0\Leftrightarrow (x-4)(4x+3)=0$
Now, $\displaystyle x-4=0\Rightarrow x=4$

or $\displaystyle 4x+3=0\Rightarrow x=-\frac{3}{4}$

Edited
(Thanks, flyingsquirrel)

5. Just a little typo :
Originally Posted by red_dog
$\displaystyle {\color{red}4}x^2-13x-12=0\Leftrightarrow {\color{red}4}x^2-16x+3x-12=0$