180=(6x+4)(8x-6)

Solution for 180=(6x+4)(8x-6) equation:

180=(6x+4)(8x-6)

We move all terms to the left:

180-((6x+4)(8x-6))=0

We multiply parentheses ..

-((+48x^2-36x+32x-24))+180=0


We calculate terms in parentheses: -((+48x^2-36x+32x-24)), so:

(+48x^2-36x+32x-24)

We get rid of parentheses

48x^2-36x+32x-24

We add all the numbers together, and all the variables

48x^2-4x-24

Back to the equation:

-(48x^2-4x-24)


We get rid of parentheses

-48x^2+4x+24+180=0

We add all the numbers together, and all the variables

-48x^2+4x+204=0

a = -48; b = 4; c = +204;
Δ = b2-4ac
Δ = 42-4·(-48)·204
Δ = 39184
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:

$\sqrt{\Delta}=\sqrt{39184}=\sqrt{16*2449}=\sqrt{16}*\sqrt{2449}=4\sqrt{2449}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2449}}{2*-48}=\frac{-4-4\sqrt{2449}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2449}}{2*-48}=\frac{-4+4\sqrt{2449}}{-96}
$