X=4(90-x)x=

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

X=4(90-X)X=

We move all terms to the left:

X-(4(90-X)X)=0

We add all the numbers together, and all the variables

X-(4(-1X+90)X)=0


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

4(-1X+90)X

We multiply parentheses

-4X^2+360X

Back to the equation:

-(-4X^2+360X)


We get rid of parentheses

4X^2-360X+X=0

We add all the numbers together, and all the variables

4X^2-359X=0

a = 4; b = -359; c = 0;
Δ = b2-4ac
Δ = -3592-4·4·0
Δ = 128881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{128881}=359$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-359)-359}{2*4}=\frac{0}{8}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-359)+359}{2*4}=\frac{718}{8}
=89+3/4
$