8x^2-6x=19

Solution for 8x^2-6x=19 equation:

8x^2-6x=19

We move all terms to the left:

8x^2-6x-(19)=0

a = 8; b = -6; c = -19;
Δ = b2-4ac
Δ = -62-4·8·(-19)
Δ = 644
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:

$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{161}}{2*8}=\frac{6-2\sqrt{161}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{161}}{2*8}=\frac{6+2\sqrt{161}}{16}
$