(6x-1)(5x+28)=180

Solution for (6x-1)(5x+28)=180 equation:

(6x-1)(5x+28)=180

We move all terms to the left:

(6x-1)(5x+28)-(180)=0

We multiply parentheses ..

(+30x^2+168x-5x-28)-180=0

We get rid of parentheses

30x^2+168x-5x-28-180=0

We add all the numbers together, and all the variables

30x^2+163x-208=0

a = 30; b = 163; c = -208;
Δ = b2-4ac
Δ = 1632-4·30·(-208)
Δ = 51529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{51529}=227$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(163)-227}{2*30}=\frac{-390}{60}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(163)+227}{2*30}=\frac{64}{60}
=1+1/15
$