2x-6x^2-3=-10

Solution for 2x-6x^2-3=-10 equation:

2x-6x^2-3=-10

We move all terms to the left:

2x-6x^2-3-(-10)=0

We add all the numbers together, and all the variables

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

a = -6; b = 2; c = +7;
Δ = b2-4ac
Δ = 22-4·(-6)·7
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{43}}{2*-6}=\frac{-2-2\sqrt{43}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{43}}{2*-6}=\frac{-2+2\sqrt{43}}{-12}
$