0.15x(x+50)-0.05(x-20)=13.5

Solution for 0.15x(x+50)-0.05(x-20)=13.5 equation:

0.15x(x+50)-0.05(x-20)=13.5

We move all terms to the left:

0.15x(x+50)-0.05(x-20)-(13.5)=0

We add all the numbers together, and all the variables

0.15x(x+50)-0.05(x-20)-13.5=0

We multiply parentheses

0x^2+0x-0.05x+1-13.5=0

We add all the numbers together, and all the variables

x^2+0.95x-12.5=0

a = 1; b = 0.95; c = -12.5;
Δ = b2-4ac
Δ = 0.952-4·1·(-12.5)
Δ = 50.9025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.95)-\sqrt{50.9025}}{2*1}=\frac{-0.95-\sqrt{50.9025}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.95)+\sqrt{50.9025}}{2*1}=\frac{-0.95+\sqrt{50.9025}}{2}
$