6x^2+x=23

Solution for 6x^2+x=23 equation:

6x^2+x=23

We move all terms to the left:

6x^2+x-(23)=0

a = 6; b = 1; c = -23;
Δ = b2-4ac
Δ = 12-4·6·(-23)
Δ = 553
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{553}}{2*6}=\frac{-1-\sqrt{553}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{553}}{2*6}=\frac{-1+\sqrt{553}}{12}
$