(6x+5)(4x+15)=120

Solution for (6x+5)(4x+15)=120 equation:

(6x+5)(4x+15)=120

We move all terms to the left:

(6x+5)(4x+15)-(120)=0

We multiply parentheses ..

(+24x^2+90x+20x+75)-120=0

We get rid of parentheses

24x^2+90x+20x+75-120=0

We add all the numbers together, and all the variables

24x^2+110x-45=0

a = 24; b = 110; c = -45;
Δ = b2-4ac
Δ = 1102-4·24·(-45)
Δ = 16420
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:

$\sqrt{\Delta}=\sqrt{16420}=\sqrt{4*4105}=\sqrt{4}*\sqrt{4105}=2\sqrt{4105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-2\sqrt{4105}}{2*24}=\frac{-110-2\sqrt{4105}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+2\sqrt{4105}}{2*24}=\frac{-110+2\sqrt{4105}}{48}
$