(11x-7)(5x-3)=118

Solution for (11x-7)(5x-3)=118 equation:

(11x-7)(5x-3)=118

We move all terms to the left:

(11x-7)(5x-3)-(118)=0

We multiply parentheses ..

(+55x^2-33x-35x+21)-118=0

We get rid of parentheses

55x^2-33x-35x+21-118=0

We add all the numbers together, and all the variables

55x^2-68x-97=0

a = 55; b = -68; c = -97;
Δ = b2-4ac
Δ = -682-4·55·(-97)
Δ = 25964
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:

$\sqrt{\Delta}=\sqrt{25964}=\sqrt{4*6491}=\sqrt{4}*\sqrt{6491}=2\sqrt{6491}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-2\sqrt{6491}}{2*55}=\frac{68-2\sqrt{6491}}{110}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+2\sqrt{6491}}{2*55}=\frac{68+2\sqrt{6491}}{110}
$