(6x+4)(5x-2)=180

Solution for (6x+4)(5x-2)=180 equation:

(6x+4)(5x-2)=180

We move all terms to the left:

(6x+4)(5x-2)-(180)=0

We multiply parentheses ..

(+30x^2-12x+20x-8)-180=0

We get rid of parentheses

30x^2-12x+20x-8-180=0

We add all the numbers together, and all the variables

30x^2+8x-188=0

a = 30; b = 8; c = -188;
Δ = b2-4ac
Δ = 82-4·30·(-188)
Δ = 22624
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:

$\sqrt{\Delta}=\sqrt{22624}=\sqrt{16*1414}=\sqrt{16}*\sqrt{1414}=4\sqrt{1414}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{1414}}{2*30}=\frac{-8-4\sqrt{1414}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{1414}}{2*30}=\frac{-8+4\sqrt{1414}}{60}
$