15x^2-10=10

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

15x^2-10=10

We move all terms to the left:

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

We add all the numbers together, and all the variables

15x^2-20=0

a = 15; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·15·(-20)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{3}}{2*15}=\frac{0-20\sqrt{3}}{30}
=-\frac{20\sqrt{3}}{30}
=-\frac{2\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{3}}{2*15}=\frac{0+20\sqrt{3}}{30}
=\frac{20\sqrt{3}}{30}
=\frac{2\sqrt{3}}{3}
$