(4x+10)(3x-5)=180

Solution for (4x+10)(3x-5)=180 equation:

(4x+10)(3x-5)=180

We move all terms to the left:

(4x+10)(3x-5)-(180)=0

We multiply parentheses ..

(+12x^2-20x+30x-50)-180=0

We get rid of parentheses

12x^2-20x+30x-50-180=0

We add all the numbers together, and all the variables

12x^2+10x-230=0

a = 12; b = 10; c = -230;
Δ = b2-4ac
Δ = 102-4·12·(-230)
Δ = 11140
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:

$\sqrt{\Delta}=\sqrt{11140}=\sqrt{4*2785}=\sqrt{4}*\sqrt{2785}=2\sqrt{2785}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{2785}}{2*12}=\frac{-10-2\sqrt{2785}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{2785}}{2*12}=\frac{-10+2\sqrt{2785}}{24}
$