(6x+7)(11x-2)(90)=180

Solution for (6x+7)(11x-2)(90)=180 equation:

(6x+7)(11x-2)(90)=180

We move all terms to the left:

(6x+7)(11x-2)(90)-(180)=0

We multiply parentheses ..

(+66x^2-12x+77x-14)90-180=0

We multiply parentheses

5940x^2-1080x+6930x-1260-180=0

We add all the numbers together, and all the variables

5940x^2+5850x-1440=0

a = 5940; b = 5850; c = -1440;
Δ = b2-4ac
Δ = 58502-4·5940·(-1440)
Δ = 68436900
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:

$\sqrt{\Delta}=\sqrt{68436900}=\sqrt{8100*8449}=\sqrt{8100}*\sqrt{8449}=90\sqrt{8449}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5850)-90\sqrt{8449}}{2*5940}=\frac{-5850-90\sqrt{8449}}{11880}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5850)+90\sqrt{8449}}{2*5940}=\frac{-5850+90\sqrt{8449}}{11880}
$