6x(4x-10)=180

Solution for 6x(4x-10)=180 equation:

6x(4x-10)=180

We move all terms to the left:

6x(4x-10)-(180)=0

We multiply parentheses

24x^2-60x-180=0

a = 24; b = -60; c = -180;
Δ = b2-4ac
Δ = -602-4·24·(-180)
Δ = 20880
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:

$\sqrt{\Delta}=\sqrt{20880}=\sqrt{144*145}=\sqrt{144}*\sqrt{145}=12\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-12\sqrt{145}}{2*24}=\frac{60-12\sqrt{145}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+12\sqrt{145}}{2*24}=\frac{60+12\sqrt{145}}{48}
$