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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+55x^2-33x-35x+21)), so:

(+55x^2-33x-35x+21)

We get rid of parentheses

55x^2-33x-35x+21

We add all the numbers together, and all the variables

55x^2-68x+21

Back to the equation:

-(55x^2-68x+21)


We get rid of parentheses

-55x^2+68x-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}
$