(x+20)(2x+10)=537.5

Solution for (x+20)(2x+10)=537.5 equation:

(x+20)(2x+10)=537.5

We move all terms to the left:

(x+20)(2x+10)-(537.5)=0

We add all the numbers together, and all the variables

(x+20)(2x+10)-537.5=0

We multiply parentheses ..

(+2x^2+10x+40x+200)-537.5=0

We get rid of parentheses

2x^2+10x+40x+200-537.5=0

We add all the numbers together, and all the variables

2x^2+50x-337.5=0

a = 2; b = 50; c = -337.5;
Δ = b2-4ac
Δ = 502-4·2·(-337.5)
Δ = 5200
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:

$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-20\sqrt{13}}{2*2}=\frac{-50-20\sqrt{13}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+20\sqrt{13}}{2*2}=\frac{-50+20\sqrt{13}}{4}
$