(2x+7)(5x-9)+(2x-7)(5x+9)=374

Solution for (2x+7)(5x-9)+(2x-7)(5x+9)=374 equation:

(2x+7)(5x-9)+(2x-7)(5x+9)=374

We move all terms to the left:

(2x+7)(5x-9)+(2x-7)(5x+9)-(374)=0

We multiply parentheses ..

(+10x^2-18x+35x-63)+(2x-7)(5x+9)-374=0

We get rid of parentheses

10x^2-18x+35x+(2x-7)(5x+9)-63-374=0

We multiply parentheses ..

10x^2+(+10x^2+18x-35x-63)-18x+35x-63-374=0

We add all the numbers together, and all the variables

10x^2+(+10x^2+18x-35x-63)+17x-437=0

We get rid of parentheses

10x^2+10x^2+18x-35x+17x-63-437=0

We add all the numbers together, and all the variables

20x^2-500=0

a = 20; b = 0; c = -500;
Δ = b2-4ac
Δ = 02-4·20·(-500)
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200}{2*20}=\frac{-200}{40}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200}{2*20}=\frac{200}{40}
=5
$