(x+5)(x+2)-3x(4x-3)=(x-5)2

Solution for (x+5)(x+2)-3x(4x-3)=(x-5)2 equation:

(x+5)(x+2)-3x(4x-3)=(x-5)2

We move all terms to the left:

(x+5)(x+2)-3x(4x-3)-((x-5)2)=0

We multiply parentheses

-12x^2+(x+5)(x+2)+9x-((x-5)2)=0

We multiply parentheses ..

-12x^2+(+x^2+2x+5x+10)+9x-((x-5)2)=0


We calculate terms in parentheses: -((x-5)2), so:

(x-5)2

We multiply parentheses

2x-10

Back to the equation:

-(2x-10)


We get rid of parentheses

-12x^2+x^2+2x+5x+9x-2x+10+10=0

We add all the numbers together, and all the variables

-11x^2+14x+20=0

a = -11; b = 14; c = +20;
Δ = b2-4ac
Δ = 142-4·(-11)·20
Δ = 1076
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:

$\sqrt{\Delta}=\sqrt{1076}=\sqrt{4*269}=\sqrt{4}*\sqrt{269}=2\sqrt{269}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{269}}{2*-11}=\frac{-14-2\sqrt{269}}{-22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{269}}{2*-11}=\frac{-14+2\sqrt{269}}{-22}
$