180=(3x+10)(6x-20)

Solution for 180=(3x+10)(6x-20) equation:

180=(3x+10)(6x-20)

We move all terms to the left:

180-((3x+10)(6x-20))=0

We multiply parentheses ..

-((+18x^2-60x+60x-200))+180=0


We calculate terms in parentheses: -((+18x^2-60x+60x-200)), so:

(+18x^2-60x+60x-200)

We get rid of parentheses

18x^2-60x+60x-200

We add all the numbers together, and all the variables

18x^2-200

Back to the equation:

-(18x^2-200)


We get rid of parentheses

-18x^2+200+180=0

We add all the numbers together, and all the variables

-18x^2+380=0

a = -18; b = 0; c = +380;
Δ = b2-4ac
Δ = 02-4·(-18)·380
Δ = 27360
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:

$\sqrt{\Delta}=\sqrt{27360}=\sqrt{144*190}=\sqrt{144}*\sqrt{190}=12\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{190}}{2*-18}=\frac{0-12\sqrt{190}}{-36}
=-\frac{12\sqrt{190}}{-36}
=-\frac{\sqrt{190}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{190}}{2*-18}=\frac{0+12\sqrt{190}}{-36}
=\frac{12\sqrt{190}}{-36}
=\frac{\sqrt{190}}{-3}
$