(6x+44)(-10x+45)=117

Solution for (6x+44)(-10x+45)=117 equation:

(6x+44)(-10x+45)=117

We move all terms to the left:

(6x+44)(-10x+45)-(117)=0

We multiply parentheses ..

(-60x^2+270x-440x+1980)-117=0

We get rid of parentheses

-60x^2+270x-440x+1980-117=0

We add all the numbers together, and all the variables

-60x^2-170x+1863=0

a = -60; b = -170; c = +1863;
Δ = b2-4ac
Δ = -1702-4·(-60)·1863
Δ = 476020
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:

$\sqrt{\Delta}=\sqrt{476020}=\sqrt{4*119005}=\sqrt{4}*\sqrt{119005}=2\sqrt{119005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-170)-2\sqrt{119005}}{2*-60}=\frac{170-2\sqrt{119005}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-170)+2\sqrt{119005}}{2*-60}=\frac{170+2\sqrt{119005}}{-120}
$