180-x=5x(90-x)+132

Solution for 180-x=5x(90-x)+132 equation:

180-x=5x(90-x)+132

We move all terms to the left:

180-x-(5x(90-x)+132)=0

We add all the numbers together, and all the variables

-x-(5x(-1x+90)+132)+180=0

We add all the numbers together, and all the variables

-1x-(5x(-1x+90)+132)+180=0


We calculate terms in parentheses: -(5x(-1x+90)+132), so:

5x(-1x+90)+132

We multiply parentheses

-5x^2+450x+132

Back to the equation:

-(-5x^2+450x+132)


We get rid of parentheses

5x^2-450x-1x-132+180=0

We add all the numbers together, and all the variables

5x^2-451x+48=0

a = 5; b = -451; c = +48;
Δ = b2-4ac
Δ = -4512-4·5·48
Δ = 202441
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{-(-451)-\sqrt{202441}}{2*5}=\frac{451-\sqrt{202441}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-451)+\sqrt{202441}}{2*5}=\frac{451+\sqrt{202441}}{10}
$