x*(6*x-7)=90

Solution for x*(6*x-7)=90 equation:

x(6x-7)=90

We move all terms to the left:

x(6x-7)-(90)=0

We multiply parentheses

6x^2-7x-90=0

a = 6; b = -7; c = -90;
Δ = b2-4ac
Δ = -72-4·6·(-90)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-47}{2*6}=\frac{-40}{12}
=-3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+47}{2*6}=\frac{54}{12}
=4+1/2
$