x(x+40)+15(2-x)=180

Solution for x(x+40)+15(2-x)=180 equation:

x(x+40)+15(2-x)=180

We move all terms to the left:

x(x+40)+15(2-x)-(180)=0

We add all the numbers together, and all the variables

x(x+40)+15(-1x+2)-180=0

We multiply parentheses

x^2+40x-15x+30-180=0

We add all the numbers together, and all the variables

x^2+25x-150=0

a = 1; b = 25; c = -150;
Δ = b2-4ac
Δ = 252-4·1·(-150)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-35}{2*1}=\frac{-60}{2}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+35}{2*1}=\frac{10}{2}
=5
$