8x^2=-5x^2+12

Solution for 8x^2=-5x^2+12 equation:

8x^2=-5x^2+12

We move all terms to the left:

8x^2-(-5x^2+12)=0

We get rid of parentheses

8x^2+5x^2-12=0

We add all the numbers together, and all the variables

13x^2-12=0

a = 13; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·13·(-12)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{39}}{2*13}=\frac{0-4\sqrt{39}}{26}
=-\frac{4\sqrt{39}}{26}
=-\frac{2\sqrt{39}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{39}}{2*13}=\frac{0+4\sqrt{39}}{26}
=\frac{4\sqrt{39}}{26}
=\frac{2\sqrt{39}}{13}
$