4x^2+x=90

Solution for 4x^2+x=90 equation:

4x^2+x=90

We move all terms to the left:

4x^2+x-(90)=0

a = 4; b = 1; c = -90;
Δ = b2-4ac
Δ = 12-4·4·(-90)
Δ = 1441
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{-(1)-\sqrt{1441}}{2*4}=\frac{-1-\sqrt{1441}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1441}}{2*4}=\frac{-1+\sqrt{1441}}{8}
$