(3x-12)(5x-34)=360

Solution for (3x-12)(5x-34)=360 equation:

(3x-12)(5x-34)=360

We move all terms to the left:

(3x-12)(5x-34)-(360)=0

We multiply parentheses ..

(+15x^2-102x-60x+408)-360=0

We get rid of parentheses

15x^2-102x-60x+408-360=0

We add all the numbers together, and all the variables

15x^2-162x+48=0

a = 15; b = -162; c = +48;
Δ = b2-4ac
Δ = -1622-4·15·48
Δ = 23364
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:

$\sqrt{\Delta}=\sqrt{23364}=\sqrt{36*649}=\sqrt{36}*\sqrt{649}=6\sqrt{649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-6\sqrt{649}}{2*15}=\frac{162-6\sqrt{649}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+6\sqrt{649}}{2*15}=\frac{162+6\sqrt{649}}{30}
$