(-8(11x^2-22x+22)+(22x-22)))=0

Solution for (-8(11x^2-22x+22)+(22x-22)))=0 equation:

(-8(11x^2-22x+22)+(22x-22)))=0


We calculate terms in parentheses: +(-8(11x^2-22x+22)+(22x-22))), so:

-8(11x^2-22x+22)+(22x-22))

We multiply parentheses

-88x^2+176x+(22x-22))-176

Back to the equation:

+(-88x^2+176x+(22x-22))-176)


We add all the numbers together, and all the variables

(-88x^2+176x+(22x-22))=0


We calculate terms in parentheses: +(-88x^2+176x+(22x-22)), so:

-88x^2+176x+(22x-22)

We get rid of parentheses

-88x^2+176x+22x-22

We add all the numbers together, and all the variables

-88x^2+198x-22

Back to the equation:

+(-88x^2+198x-22)


We get rid of parentheses

-88x^2+198x-22=0

a = -88; b = 198; c = -22;
Δ = b2-4ac
Δ = 1982-4·(-88)·(-22)
Δ = 31460
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:

$\sqrt{\Delta}=\sqrt{31460}=\sqrt{484*65}=\sqrt{484}*\sqrt{65}=22\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(198)-22\sqrt{65}}{2*-88}=\frac{-198-22\sqrt{65}}{-176}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(198)+22\sqrt{65}}{2*-88}=\frac{-198+22\sqrt{65}}{-176}
$