180-x=4x(90-x)

Solution for 180-x=4x(90-x) equation:

180-x=4x(90-x)

We move all terms to the left:

180-x-(4x(90-x))=0

We add all the numbers together, and all the variables

-x-(4x(-1x+90))+180=0

We add all the numbers together, and all the variables

-1x-(4x(-1x+90))+180=0


We calculate terms in parentheses: -(4x(-1x+90)), so:

4x(-1x+90)

We multiply parentheses

-4x^2+360x

Back to the equation:

-(-4x^2+360x)


We get rid of parentheses

4x^2-360x-1x+180=0

We add all the numbers together, and all the variables

4x^2-361x+180=0

a = 4; b = -361; c = +180;
Δ = b2-4ac
Δ = -3612-4·4·180
Δ = 127441
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{-(-361)-\sqrt{127441}}{2*4}=\frac{361-\sqrt{127441}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-361)+\sqrt{127441}}{2*4}=\frac{361+\sqrt{127441}}{8}
$