7.5=6x^2-2x

Solution for 7.5=6x^2-2x equation:

7.5=6x^2-2x

We move all terms to the left:

7.5-(6x^2-2x)=0

We get rid of parentheses

-6x^2+2x+7.5=0

a = -6; b = 2; c = +7.5;
Δ = b2-4ac
Δ = 22-4·(-6)·7.5
Δ = 184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{46}}{2*-6}=\frac{-2-2\sqrt{46}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{46}}{2*-6}=\frac{-2+2\sqrt{46}}{-12}
$