15x^2-5=7

Solution for 15x^2-5=7 equation:

15x^2-5=7

We move all terms to the left:

15x^2-5-(7)=0

We add all the numbers together, and all the variables

15x^2-12=0

a = 15; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·15·(-12)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*15}=\frac{0-12\sqrt{5}}{30}
=-\frac{12\sqrt{5}}{30}
=-\frac{2\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*15}=\frac{0+12\sqrt{5}}{30}
=\frac{12\sqrt{5}}{30}
=\frac{2\sqrt{5}}{5}
$