(20+2x)(50+2x)=456

Solution for (20+2x)(50+2x)=456 equation:

(20+2x)(50+2x)=456

We move all terms to the left:

(20+2x)(50+2x)-(456)=0

We add all the numbers together, and all the variables

(2x+20)(2x+50)-456=0

We multiply parentheses ..

(+4x^2+100x+40x+1000)-456=0

We get rid of parentheses

4x^2+100x+40x+1000-456=0

We add all the numbers together, and all the variables

4x^2+140x+544=0

a = 4; b = 140; c = +544;
Δ = b2-4ac
Δ = 1402-4·4·544
Δ = 10896
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:

$\sqrt{\Delta}=\sqrt{10896}=\sqrt{16*681}=\sqrt{16}*\sqrt{681}=4\sqrt{681}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-4\sqrt{681}}{2*4}=\frac{-140-4\sqrt{681}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+4\sqrt{681}}{2*4}=\frac{-140+4\sqrt{681}}{8}
$