-8x^2+10=-25x^2+14

Solution for -8x^2+10=-25x^2+14 equation:

-8x^2+10=-25x^2+14

We move all terms to the left:

-8x^2+10-(-25x^2+14)=0

We get rid of parentheses

-8x^2+25x^2-14+10=0

We add all the numbers together, and all the variables

17x^2-4=0

a = 17; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·17·(-4)
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{17}}{2*17}=\frac{0-4\sqrt{17}}{34}
=-\frac{4\sqrt{17}}{34}
=-\frac{2\sqrt{17}}{17}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{17}}{2*17}=\frac{0+4\sqrt{17}}{34}
=\frac{4\sqrt{17}}{34}
=\frac{2\sqrt{17}}{17}
$