# Thread: Quadratic Equation Problems

1. ## Quadratic Equation Problems

1) Solve by factoring:

$(u+3)/(2u-7)=(2u-1)/(u-3)$

2) Find the exact solution to:

$2(k-1)]=(4-5k)/(k+1)$

3) Solve this equation:

$(3t)/(t^2-6)=Sqrt3$

2. 1) $\frac {u+3}{2u-7} = \frac {2u-1}{u-3}$

Cross Multiply to get:

$
\frac {(u + 3)(u - 3)}{2u - 7} = 2u - 1$

Multiply both sides by $2u - 7$:

$(u + 3)(u - 3) = (2u - 7)(2u - 1)$

Now multiply out:

$u^2 + 3u - 3u - 9 = 4u^2 - 2u - 14u + 7$

Move everything to one side, then simplify:

$-3u^2 + 16u -16 = 0$

Now use the quadratic equation to find the roots.

2) $2k - 2 = \frac {4 - 5k}{k + 1}$

Multiply both sides by $k + 1$:

(2k - 2)(k + 1) = 4 - 5k

Multiply out:

$
2k^2 + 2k - 2k - 2 = 4 - 5k$

Bring everything to one side, then simplify:

$2k^2 + 5k - 6 = 0$

Now use the quadratic equation.

3)