180-x=42x(90-x)

Solution for 180-x=42x(90-x) equation:

180-x=42x(90-x)

We move all terms to the left:

180-x-(42x(90-x))=0

We add all the numbers together, and all the variables

-x-(42x(-1x+90))+180=0

We add all the numbers together, and all the variables

-1x-(42x(-1x+90))+180=0


We calculate terms in parentheses: -(42x(-1x+90)), so:

42x(-1x+90)

We multiply parentheses

-42x^2+3780x

Back to the equation:

-(-42x^2+3780x)


We get rid of parentheses

42x^2-3780x-1x+180=0

We add all the numbers together, and all the variables

42x^2-3781x+180=0

a = 42; b = -3781; c = +180;
Δ = b2-4ac
Δ = -37812-4·42·180
Δ = 14265721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14265721}=\sqrt{7921*1801}=\sqrt{7921}*\sqrt{1801}=89\sqrt{1801}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3781)-89\sqrt{1801}}{2*42}=\frac{3781-89\sqrt{1801}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3781)+89\sqrt{1801}}{2*42}=\frac{3781+89\sqrt{1801}}{84}
$