10x(3x-6)=9

Solution for 10x(3x-6)=9 equation:

10x(3x-6)=9

We move all terms to the left:

10x(3x-6)-(9)=0

We multiply parentheses

30x^2-60x-9=0

a = 30; b = -60; c = -9;
Δ = b2-4ac
Δ = -602-4·30·(-9)
Δ = 4680
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:

$\sqrt{\Delta}=\sqrt{4680}=\sqrt{36*130}=\sqrt{36}*\sqrt{130}=6\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-6\sqrt{130}}{2*30}=\frac{60-6\sqrt{130}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+6\sqrt{130}}{2*30}=\frac{60+6\sqrt{130}}{60}
$