8x^2-12x-10=2x+5

Solution for 8x^2-12x-10=2x+5 equation:

8x^2-12x-10=2x+5

We move all terms to the left:

8x^2-12x-10-(2x+5)=0

We get rid of parentheses

8x^2-12x-2x-5-10=0

We add all the numbers together, and all the variables

8x^2-14x-15=0

a = 8; b = -14; c = -15;
Δ = b2-4ac
Δ = -142-4·8·(-15)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-26}{2*8}=\frac{-12}{16}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+26}{2*8}=\frac{40}{16}
=2+1/2
$