(2x-9)(x-8)+(x-8)(15+x)=0

Solution for (2x-9)(x-8)+(x-8)(15+x)=0 equation:

(2x-9)(x-8)+(x-8)(15+x)=0

We add all the numbers together, and all the variables

(2x-9)(x-8)+(x-8)(x+15)=0

We multiply parentheses ..

(+2x^2-16x-9x+72)+(x-8)(x+15)=0

We get rid of parentheses

2x^2-16x-9x+(x-8)(x+15)+72=0

We multiply parentheses ..

2x^2+(+x^2+15x-8x-120)-16x-9x+72=0

We add all the numbers together, and all the variables

2x^2+(+x^2+15x-8x-120)-25x+72=0

We get rid of parentheses

2x^2+x^2+15x-8x-25x-120+72=0

We add all the numbers together, and all the variables

3x^2-18x-48=0

a = 3; b = -18; c = -48;
Δ = b2-4ac
Δ = -182-4·3·(-48)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-30}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+30}{2*3}=\frac{48}{6}
=8
$