(10+2x)(11x+1)=252

Solution for (10+2x)(11x+1)=252 equation:

(10+2x)(11x+1)=252

We move all terms to the left:

(10+2x)(11x+1)-(252)=0

We add all the numbers together, and all the variables

(2x+10)(11x+1)-252=0

We multiply parentheses ..

(+22x^2+2x+110x+10)-252=0

We get rid of parentheses

22x^2+2x+110x+10-252=0

We add all the numbers together, and all the variables

22x^2+112x-242=0

a = 22; b = 112; c = -242;
Δ = b2-4ac
Δ = 1122-4·22·(-242)
Δ = 33840
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:

$\sqrt{\Delta}=\sqrt{33840}=\sqrt{144*235}=\sqrt{144}*\sqrt{235}=12\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-12\sqrt{235}}{2*22}=\frac{-112-12\sqrt{235}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+12\sqrt{235}}{2*22}=\frac{-112+12\sqrt{235}}{44}
$