(5x-11)(3x+17)=118

Solution for (5x-11)(3x+17)=118 equation:

(5x-11)(3x+17)=118

We move all terms to the left:

(5x-11)(3x+17)-(118)=0

We multiply parentheses ..

(+15x^2+85x-33x-187)-118=0

We get rid of parentheses

15x^2+85x-33x-187-118=0

We add all the numbers together, and all the variables

15x^2+52x-305=0

a = 15; b = 52; c = -305;
Δ = b2-4ac
Δ = 522-4·15·(-305)
Δ = 21004
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:

$\sqrt{\Delta}=\sqrt{21004}=\sqrt{4*5251}=\sqrt{4}*\sqrt{5251}=2\sqrt{5251}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-2\sqrt{5251}}{2*15}=\frac{-52-2\sqrt{5251}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+2\sqrt{5251}}{2*15}=\frac{-52+2\sqrt{5251}}{30}
$