7(x-3)(11x-73)=90

Solution for 7(x-3)(11x-73)=90 equation:

7(x-3)(11x-73)=90

We move all terms to the left:

7(x-3)(11x-73)-(90)=0

We multiply parentheses ..

7(+11x^2-73x-33x+219)-90=0

We multiply parentheses

77x^2-511x-231x+1533-90=0

We add all the numbers together, and all the variables

77x^2-742x+1443=0

a = 77; b = -742; c = +1443;
Δ = b2-4ac
Δ = -7422-4·77·1443
Δ = 106120
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:

$\sqrt{\Delta}=\sqrt{106120}=\sqrt{4*26530}=\sqrt{4}*\sqrt{26530}=2\sqrt{26530}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-742)-2\sqrt{26530}}{2*77}=\frac{742-2\sqrt{26530}}{154}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-742)+2\sqrt{26530}}{2*77}=\frac{742+2\sqrt{26530}}{154}
$