x=2x(90-x)+8-30

Solution for x=2x(90-x)+8-30 equation:

x=2x(90-x)+8-30

We move all terms to the left:

x-(2x(90-x)+8-30)=0

We add all the numbers together, and all the variables

x-(2x(-1x+90)+8-30)=0


We calculate terms in parentheses: -(2x(-1x+90)+8-30), so:

2x(-1x+90)+8-30

We add all the numbers together, and all the variables

2x(-1x+90)-22

We multiply parentheses

-2x^2+180x-22

Back to the equation:

-(-2x^2+180x-22)


We get rid of parentheses

2x^2-180x+x+22=0

We add all the numbers together, and all the variables

2x^2-179x+22=0

a = 2; b = -179; c = +22;
Δ = b2-4ac
Δ = -1792-4·2·22
Δ = 31865
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{-(-179)-\sqrt{31865}}{2*2}=\frac{179-\sqrt{31865}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-179)+\sqrt{31865}}{2*2}=\frac{179+\sqrt{31865}}{4}
$