(x+5)(2x+7)-(x+5)(x-3)=0

Solution for (x+5)(2x+7)-(x+5)(x-3)=0 equation:

(x+5)(2x+7)-(x+5)(x-3)=0

We multiply parentheses ..

(+2x^2+7x+10x+35)-(x+5)(x-3)=0

We get rid of parentheses

2x^2+7x+10x-(x+5)(x-3)+35=0

We multiply parentheses ..

2x^2-(+x^2-3x+5x-15)+7x+10x+35=0

We add all the numbers together, and all the variables

2x^2-(+x^2-3x+5x-15)+17x+35=0

We get rid of parentheses

2x^2-x^2+3x-5x+17x+15+35=0

We add all the numbers together, and all the variables

x^2+15x+50=0

a = 1; b = 15; c = +50;
Δ = b2-4ac
Δ = 152-4·1·50
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5}{2*1}=\frac{-20}{2}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5}{2*1}=\frac{-10}{2}
=-5
$