(x)(4x-9)=90

Solution for (x)(4x-9)=90 equation:

(x)(4x-9)=90

We move all terms to the left:

(x)(4x-9)-(90)=0

We multiply parentheses

4x^2-9x-90=0

a = 4; b = -9; c = -90;
Δ = b2-4ac
Δ = -92-4·4·(-90)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-39}{2*4}=\frac{-30}{8}
=-3+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+39}{2*4}=\frac{48}{8}
=6
$