(3x-1)(2x-9)=90

Solution for (3x-1)(2x-9)=90 equation:

(3x-1)(2x-9)=90

We move all terms to the left:

(3x-1)(2x-9)-(90)=0

We multiply parentheses ..

(+6x^2-27x-2x+9)-90=0

We get rid of parentheses

6x^2-27x-2x+9-90=0

We add all the numbers together, and all the variables

6x^2-29x-81=0

a = 6; b = -29; c = -81;
Δ = b2-4ac
Δ = -292-4·6·(-81)
Δ = 2785
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{-(-29)-\sqrt{2785}}{2*6}=\frac{29-\sqrt{2785}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{2785}}{2*6}=\frac{29+\sqrt{2785}}{12}
$