(5x+50)(x+100)=500

Solution for (5x+50)(x+100)=500 equation:

(5x+50)(x+100)=500

We move all terms to the left:

(5x+50)(x+100)-(500)=0

We multiply parentheses ..

(+5x^2+500x+50x+5000)-500=0

We get rid of parentheses

5x^2+500x+50x+5000-500=0

We add all the numbers together, and all the variables

5x^2+550x+4500=0

a = 5; b = 550; c = +4500;
Δ = b2-4ac
Δ = 5502-4·5·4500
Δ = 212500
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:

$\sqrt{\Delta}=\sqrt{212500}=\sqrt{2500*85}=\sqrt{2500}*\sqrt{85}=50\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(550)-50\sqrt{85}}{2*5}=\frac{-550-50\sqrt{85}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(550)+50\sqrt{85}}{2*5}=\frac{-550+50\sqrt{85}}{10}
$