7=6x^2-x

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

7=6x^2-x

We move all terms to the left:

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

We get rid of parentheses

-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
$