-3-6x^2=-43

Solution for -3-6x^2=-43 equation:

-3-6x^2=-43

We move all terms to the left:

-3-6x^2-(-43)=0

We add all the numbers together, and all the variables

-6x^2+40=0

a = -6; b = 0; c = +40;
Δ = b2-4ac
Δ = 02-4·(-6)·40
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*-6}=\frac{0-8\sqrt{15}}{-12}
=-\frac{8\sqrt{15}}{-12}
=-\frac{2\sqrt{15}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*-6}=\frac{0+8\sqrt{15}}{-12}
=\frac{8\sqrt{15}}{-12}
=\frac{2\sqrt{15}}{-3}
$