x(3x-26)=90

Solution for x(3x-26)=90 equation:

x(3x-26)=90

We move all terms to the left:

x(3x-26)-(90)=0

We multiply parentheses

3x^2-26x-90=0

a = 3; b = -26; c = -90;
Δ = b2-4ac
Δ = -262-4·3·(-90)
Δ = 1756
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:

$\sqrt{\Delta}=\sqrt{1756}=\sqrt{4*439}=\sqrt{4}*\sqrt{439}=2\sqrt{439}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{439}}{2*3}=\frac{26-2\sqrt{439}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{439}}{2*3}=\frac{26+2\sqrt{439}}{6}
$