X=90(x+22)(2+3x)

Solution for X=90(x+22)(2+3x) equation:

X=90(X+22)(2+3X)

We move all terms to the left:

X-(90(X+22)(2+3X))=0

We add all the numbers together, and all the variables

X-(90(X+22)(3X+2))=0

We multiply parentheses ..

-(90(+3X^2+2X+66X+44))+X=0


We calculate terms in parentheses: -(90(+3X^2+2X+66X+44)), so:

90(+3X^2+2X+66X+44)

We multiply parentheses

270X^2+180X+5940X+3960

We add all the numbers together, and all the variables

270X^2+6120X+3960

Back to the equation:

-(270X^2+6120X+3960)


We add all the numbers together, and all the variables

X-(270X^2+6120X+3960)=0

We get rid of parentheses

-270X^2+X-6120X-3960=0

We add all the numbers together, and all the variables

-270X^2-6119X-3960=0

a = -270; b = -6119; c = -3960;
Δ = b2-4ac
Δ = -61192-4·(-270)·(-3960)
Δ = 33165361
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{-(-6119)-\sqrt{33165361}}{2*-270}=\frac{6119-\sqrt{33165361}}{-540}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6119)+\sqrt{33165361}}{2*-270}=\frac{6119+\sqrt{33165361}}{-540}
$