(11x-5)2-(10x-1)2-(3x-20)(7x+10)=124

Solution for (11x-5)2-(10x-1)2-(3x-20)(7x+10)=124 equation:

(11x-5)2-(10x-1)2-(3x-20)(7x+10)=124

We move all terms to the left:

(11x-5)2-(10x-1)2-(3x-20)(7x+10)-(124)=0

We multiply parentheses

22x-20x-(3x-20)(7x+10)-10+2-124=0

We multiply parentheses ..

-(+21x^2+30x-140x-200)+22x-20x-10+2-124=0

We add all the numbers together, and all the variables

-(+21x^2+30x-140x-200)+2x-132=0

We get rid of parentheses

-21x^2-30x+140x+2x+200-132=0

We add all the numbers together, and all the variables

-21x^2+112x+68=0

a = -21; b = 112; c = +68;
Δ = b2-4ac
Δ = 1122-4·(-21)·68
Δ = 18256
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:

$\sqrt{\Delta}=\sqrt{18256}=\sqrt{16*1141}=\sqrt{16}*\sqrt{1141}=4\sqrt{1141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-4\sqrt{1141}}{2*-21}=\frac{-112-4\sqrt{1141}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+4\sqrt{1141}}{2*-21}=\frac{-112+4\sqrt{1141}}{-42}
$