(2x-3)x=90

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

(2x-3)x=90

We move all terms to the left:

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

We multiply parentheses

2x^2-3x-90=0

a = 2; b = -3; c = -90;
Δ = b2-4ac
Δ = -32-4·2·(-90)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-27}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+27}{2*2}=\frac{30}{4}
=7+1/2
$