(3x+10)(5x-12)=180

Solution for (3x+10)(5x-12)=180 equation:

(3x+10)(5x-12)=180

We move all terms to the left:

(3x+10)(5x-12)-(180)=0

We multiply parentheses ..

(+15x^2-36x+50x-120)-180=0

We get rid of parentheses

15x^2-36x+50x-120-180=0

We add all the numbers together, and all the variables

15x^2+14x-300=0

a = 15; b = 14; c = -300;
Δ = b2-4ac
Δ = 142-4·15·(-300)
Δ = 18196
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:

$\sqrt{\Delta}=\sqrt{18196}=\sqrt{4*4549}=\sqrt{4}*\sqrt{4549}=2\sqrt{4549}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{4549}}{2*15}=\frac{-14-2\sqrt{4549}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{4549}}{2*15}=\frac{-14+2\sqrt{4549}}{30}
$