3x^2+13x+23=90

Solution for 3x^2+13x+23=90 equation:

3x^2+13x+23=90

We move all terms to the left:

3x^2+13x+23-(90)=0

We add all the numbers together, and all the variables

3x^2+13x-67=0

a = 3; b = 13; c = -67;
Δ = b2-4ac
Δ = 132-4·3·(-67)
Δ = 973
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{-(13)-\sqrt{973}}{2*3}=\frac{-13-\sqrt{973}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{973}}{2*3}=\frac{-13+\sqrt{973}}{6}
$