15-6x^2=10

Solution for 15-6x^2=10 equation:

15-6x^2=10

We move all terms to the left:

15-6x^2-(10)=0

We add all the numbers together, and all the variables

-6x^2+5=0

a = -6; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-6)·5
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*-6}=\frac{0-2\sqrt{30}}{-12}
=-\frac{2\sqrt{30}}{-12}
=-\frac{\sqrt{30}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*-6}=\frac{0+2\sqrt{30}}{-12}
=\frac{2\sqrt{30}}{-12}
=\frac{\sqrt{30}}{-6}
$