(4x+10)(3x-6)=60

Solution for (4x+10)(3x-6)=60 equation:

(4x+10)(3x-6)=60

We move all terms to the left:

(4x+10)(3x-6)-(60)=0

We multiply parentheses ..

(+12x^2-24x+30x-60)-60=0

We get rid of parentheses

12x^2-24x+30x-60-60=0

We add all the numbers together, and all the variables

12x^2+6x-120=0

a = 12; b = 6; c = -120;
Δ = b2-4ac
Δ = 62-4·12·(-120)
Δ = 5796
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:

$\sqrt{\Delta}=\sqrt{5796}=\sqrt{36*161}=\sqrt{36}*\sqrt{161}=6\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{161}}{2*12}=\frac{-6-6\sqrt{161}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{161}}{2*12}=\frac{-6+6\sqrt{161}}{24}
$