18x-180-x^2+10x=5x-60

Solution for 18x-180-x^2+10x=5x-60 equation:

18x-180-x^2+10x=5x-60

We move all terms to the left:

18x-180-x^2+10x-(5x-60)=0

We add all the numbers together, and all the variables

-1x^2+28x-(5x-60)-180=0

We get rid of parentheses

-1x^2+28x-5x+60-180=0

We add all the numbers together, and all the variables

-1x^2+23x-120=0

a = -1; b = 23; c = -120;
Δ = b2-4ac
Δ = 232-4·(-1)·(-120)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-7}{2*-1}=\frac{-30}{-2}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+7}{2*-1}=\frac{-16}{-2}
=+8
$