-2x^2-6x=-7

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

-2x^2-6x=-7

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

a = -2; b = -6; c = +7;
Δ = b2-4ac
Δ = -62-4·(-2)·7
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{23}}{2*-2}=\frac{6-2\sqrt{23}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{23}}{2*-2}=\frac{6+2\sqrt{23}}{-4}
$