8x^2-19x=6

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

8x^2-19x=6

We move all terms to the left:

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

a = 8; b = -19; c = -6;
Δ = b2-4ac
Δ = -192-4·8·(-6)
Δ = 553
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{553}}{2*8}=\frac{19-\sqrt{553}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{553}}{2*8}=\frac{19+\sqrt{553}}{16}
$