(5x+50)(10x+90)=55

Solution for (5x+50)(10x+90)=55 equation:

(5x+50)(10x+90)=55

We move all terms to the left:

(5x+50)(10x+90)-(55)=0

We multiply parentheses ..

(+50x^2+450x+500x+4500)-55=0

We get rid of parentheses

50x^2+450x+500x+4500-55=0

We add all the numbers together, and all the variables

50x^2+950x+4445=0

a = 50; b = 950; c = +4445;
Δ = b2-4ac
Δ = 9502-4·50·4445
Δ = 13500
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:

$\sqrt{\Delta}=\sqrt{13500}=\sqrt{900*15}=\sqrt{900}*\sqrt{15}=30\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(950)-30\sqrt{15}}{2*50}=\frac{-950-30\sqrt{15}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(950)+30\sqrt{15}}{2*50}=\frac{-950+30\sqrt{15}}{100}
$