(8x^2-6x-38)=2x-5

Solution for (8x^2-6x-38)=2x-5 equation:

(8x^2-6x-38)=2x-5

We move all terms to the left:

(8x^2-6x-38)-(2x-5)=0

We get rid of parentheses

8x^2-6x-2x-38+5=0

We add all the numbers together, and all the variables

8x^2-8x-33=0

a = 8; b = -8; c = -33;
Δ = b2-4ac
Δ = -82-4·8·(-33)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{70}}{2*8}=\frac{8-4\sqrt{70}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{70}}{2*8}=\frac{8+4\sqrt{70}}{16}
$