90(3x+2)x=1

Solution for 90(3x+2)x=1 equation:

90(3x+2)x=1

We move all terms to the left:

90(3x+2)x-(1)=0

We multiply parentheses

270x^2+180x-1=0

a = 270; b = 180; c = -1;
Δ = b2-4ac
Δ = 1802-4·270·(-1)
Δ = 33480
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:

$\sqrt{\Delta}=\sqrt{33480}=\sqrt{36*930}=\sqrt{36}*\sqrt{930}=6\sqrt{930}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-6\sqrt{930}}{2*270}=\frac{-180-6\sqrt{930}}{540}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+6\sqrt{930}}{2*270}=\frac{-180+6\sqrt{930}}{540}
$