x(3x-5)=90

Solution for x(3x-5)=90 equation:

x(3x-5)=90

We move all terms to the left:

x(3x-5)-(90)=0

We multiply parentheses

3x^2-5x-90=0

a = 3; b = -5; c = -90;
Δ = b2-4ac
Δ = -52-4·3·(-90)
Δ = 1105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{1105}}{2*3}=\frac{5-\sqrt{1105}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{1105}}{2*3}=\frac{5+\sqrt{1105}}{6}
$