6x^2+x=7

Solution for 6x^2+x=7 equation:

6x^2+x=7

We move all terms to the left:

6x^2+x-(7)=0

a = 6; b = 1; c = -7;
Δ = b2-4ac
Δ = 12-4·6·(-7)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-13}{2*6}=\frac{-14}{12}
=-1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+13}{2*6}=\frac{12}{12}
=1
$