8x^2+14x-17=2x^2-3

Solution for 8x^2+14x-17=2x^2-3 equation:

8x^2+14x-17=2x^2-3

We move all terms to the left:

8x^2+14x-17-(2x^2-3)=0

We get rid of parentheses

8x^2-2x^2+14x+3-17=0

We add all the numbers together, and all the variables

6x^2+14x-14=0

a = 6; b = 14; c = -14;
Δ = b2-4ac
Δ = 142-4·6·(-14)
Δ = 532
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:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{133}}{2*6}=\frac{-14-2\sqrt{133}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{133}}{2*6}=\frac{-14+2\sqrt{133}}{12}
$