10x(9x+3)=12

Solution for 10x(9x+3)=12 equation:

10x(9x+3)=12

We move all terms to the left:

10x(9x+3)-(12)=0

We multiply parentheses

90x^2+30x-12=0

a = 90; b = 30; c = -12;
Δ = b2-4ac
Δ = 302-4·90·(-12)
Δ = 5220
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:

$\sqrt{\Delta}=\sqrt{5220}=\sqrt{36*145}=\sqrt{36}*\sqrt{145}=6\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{145}}{2*90}=\frac{-30-6\sqrt{145}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{145}}{2*90}=\frac{-30+6\sqrt{145}}{180}
$