42=x(180-x)

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

42=x(180-x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(x(-1x+180)), so:

x(-1x+180)

We multiply parentheses

-1x^2+180x

Back to the equation:

-(-1x^2+180x)


We get rid of parentheses

1x^2-180x+42=0

We add all the numbers together, and all the variables

x^2-180x+42=0

a = 1; b = -180; c = +42;
Δ = b2-4ac
Δ = -1802-4·1·42
Δ = 32232
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:

$\sqrt{\Delta}=\sqrt{32232}=\sqrt{4*8058}=\sqrt{4}*\sqrt{8058}=2\sqrt{8058}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-2\sqrt{8058}}{2*1}=\frac{180-2\sqrt{8058}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+2\sqrt{8058}}{2*1}=\frac{180+2\sqrt{8058}}{2}
$