7x^2+3=-x^2+15

Solution for 7x^2+3=-x^2+15 equation:

7x^2+3=-x^2+15

We move all terms to the left:

7x^2+3-(-x^2+15)=0

We get rid of parentheses

7x^2+x^2-15+3=0

We add all the numbers together, and all the variables

8x^2-12=0

a = 8; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·8·(-12)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*8}=\frac{0-8\sqrt{6}}{16}
=-\frac{8\sqrt{6}}{16}
=-\frac{\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*8}=\frac{0+8\sqrt{6}}{16}
=\frac{8\sqrt{6}}{16}
=\frac{\sqrt{6}}{2}
$