8x^2-3=8x+10

Solution for 8x^2-3=8x+10 equation:

8x^2-3=8x+10

We move all terms to the left:

8x^2-3-(8x+10)=0

We get rid of parentheses

8x^2-8x-10-3=0

We add all the numbers together, and all the variables

8x^2-8x-13=0

a = 8; b = -8; c = -13;
Δ = b2-4ac
Δ = -82-4·8·(-13)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{30}}{2*8}=\frac{8-4\sqrt{30}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{30}}{2*8}=\frac{8+4\sqrt{30}}{16}
$