(50+2x)(30+2x)=900

Solution for (50+2x)(30+2x)=900 equation:

(50+2x)(30+2x)=900

We move all terms to the left:

(50+2x)(30+2x)-(900)=0

We add all the numbers together, and all the variables

(2x+50)(2x+30)-900=0

We multiply parentheses ..

(+4x^2+60x+100x+1500)-900=0

We get rid of parentheses

4x^2+60x+100x+1500-900=0

We add all the numbers together, and all the variables

4x^2+160x+600=0

a = 4; b = 160; c = +600;
Δ = b2-4ac
Δ = 1602-4·4·600
Δ = 16000
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:

$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-40\sqrt{10}}{2*4}=\frac{-160-40\sqrt{10}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+40\sqrt{10}}{2*4}=\frac{-160+40\sqrt{10}}{8}
$