-x^2+5x+24=2x-64

Solution for -x^2+5x+24=2x-64 equation:

-x^2+5x+24=2x-64

We move all terms to the left:

-x^2+5x+24-(2x-64)=0

We add all the numbers together, and all the variables

-1x^2+5x-(2x-64)+24=0

We get rid of parentheses

-1x^2+5x-2x+64+24=0

We add all the numbers together, and all the variables

-1x^2+3x+88=0

a = -1; b = 3; c = +88;
Δ = b2-4ac
Δ = 32-4·(-1)·88
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-19}{2*-1}=\frac{-22}{-2}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+19}{2*-1}=\frac{16}{-2}
=-8
$