2x-3+3x2=90

Solution for 2x-3+3x2=90 equation:

2x-3+3x^2=90

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x^2+2x-93=0

a = 3; b = 2; c = -93;
Δ = b2-4ac
Δ = 22-4·3·(-93)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{70}}{2*3}=\frac{-2-4\sqrt{70}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{70}}{2*3}=\frac{-2+4\sqrt{70}}{6}
$