(X+20)=(96-x)x=

Solution for (X+20)=(96-x)x= equation:

(X+20)=(96-X)X=

We move all terms to the left:

(X+20)-((96-X)X)=0

We add all the numbers together, and all the variables

(X+20)-((-1X+96)X)=0

We get rid of parentheses

X-((-1X+96)X)+20=0


We calculate terms in parentheses: -((-1X+96)X), so:

(-1X+96)X

We multiply parentheses

-1X^2+96X

Back to the equation:

-(-1X^2+96X)


We get rid of parentheses

1X^2-96X+X+20=0

We add all the numbers together, and all the variables

X^2-95X+20=0

a = 1; b = -95; c = +20;
Δ = b2-4ac
Δ = -952-4·1·20
Δ = 8945
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{-(-95)-\sqrt{8945}}{2*1}=\frac{95-\sqrt{8945}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95)+\sqrt{8945}}{2*1}=\frac{95+\sqrt{8945}}{2}
$