(x-9)(2x-5)+(x-7)(2x+4)-(3x^2+13x-8)=0

Solution for (x-9)(2x-5)+(x-7)(2x+4)-(3x^2+13x-8)=0 equation:

(x-9)(2x-5)+(x-7)(2x+4)-(3x^2+13x-8)=0

We get rid of parentheses

-3x^2+(x-9)(2x-5)+(x-7)(2x+4)-13x+8=0

We multiply parentheses ..

-3x^2+(+2x^2-5x-18x+45)+(x-7)(2x+4)-13x+8=0

We add all the numbers together, and all the variables

-3x^2+(+2x^2-5x-18x+45)-13x+(x-7)(2x+4)+8=0

We get rid of parentheses

-3x^2+2x^2-5x-18x-13x+(x-7)(2x+4)+45+8=0

We multiply parentheses ..

-3x^2+2x^2+(+2x^2+4x-14x-28)-5x-18x-13x+45+8=0

We add all the numbers together, and all the variables

-1x^2+(+2x^2+4x-14x-28)-36x+53=0

We get rid of parentheses

-1x^2+2x^2+4x-14x-36x-28+53=0

We add all the numbers together, and all the variables

x^2-46x+25=0

a = 1; b = -46; c = +25;
Δ = b2-4ac
Δ = -462-4·1·25
Δ = 2016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-12\sqrt{14}}{2*1}=\frac{46-12\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+12\sqrt{14}}{2*1}=\frac{46+12\sqrt{14}}{2}
$