6x(4x-10)=90

Solution for 6x(4x-10)=90 equation:

6x(4x-10)=90

We move all terms to the left:

6x(4x-10)-(90)=0

We multiply parentheses

24x^2-60x-90=0

a = 24; b = -60; c = -90;
Δ = b2-4ac
Δ = -602-4·24·(-90)
Δ = 12240
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:

$\sqrt{\Delta}=\sqrt{12240}=\sqrt{144*85}=\sqrt{144}*\sqrt{85}=12\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-12\sqrt{85}}{2*24}=\frac{60-12\sqrt{85}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+12\sqrt{85}}{2*24}=\frac{60+12\sqrt{85}}{48}
$