X=(9x+5)*(6x-6)

Solution for X=(9x+5)*(6x-6) equation:

X=(9X+5)(6X-6)

We move all terms to the left:

X-((9X+5)(6X-6))=0

We multiply parentheses ..

-((+54X^2-54X+30X-30))+X=0


We calculate terms in parentheses: -((+54X^2-54X+30X-30)), so:

(+54X^2-54X+30X-30)

We get rid of parentheses

54X^2-54X+30X-30

We add all the numbers together, and all the variables

54X^2-24X-30

Back to the equation:

-(54X^2-24X-30)


We add all the numbers together, and all the variables

X-(54X^2-24X-30)=0

We get rid of parentheses

-54X^2+X+24X+30=0

We add all the numbers together, and all the variables

-54X^2+25X+30=0

a = -54; b = 25; c = +30;
Δ = b2-4ac
Δ = 252-4·(-54)·30
Δ = 7105
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:

$\sqrt{\Delta}=\sqrt{7105}=\sqrt{49*145}=\sqrt{49}*\sqrt{145}=7\sqrt{145}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-7\sqrt{145}}{2*-54}=\frac{-25-7\sqrt{145}}{-108}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+7\sqrt{145}}{2*-54}=\frac{-25+7\sqrt{145}}{-108}
$