(5x+1)(12x-28)=360

Solution for (5x+1)(12x-28)=360 equation:

(5x+1)(12x-28)=360

We move all terms to the left:

(5x+1)(12x-28)-(360)=0

We multiply parentheses ..

(+60x^2-140x+12x-28)-360=0

We get rid of parentheses

60x^2-140x+12x-28-360=0

We add all the numbers together, and all the variables

60x^2-128x-388=0

a = 60; b = -128; c = -388;
Δ = b2-4ac
Δ = -1282-4·60·(-388)
Δ = 109504
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:

$\sqrt{\Delta}=\sqrt{109504}=\sqrt{64*1711}=\sqrt{64}*\sqrt{1711}=8\sqrt{1711}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-8\sqrt{1711}}{2*60}=\frac{128-8\sqrt{1711}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+8\sqrt{1711}}{2*60}=\frac{128+8\sqrt{1711}}{120}
$