2x^2-12x=19

Solution for 2x^2-12x=19 equation:

2x^2-12x=19

We move all terms to the left:

2x^2-12x-(19)=0

a = 2; b = -12; c = -19;
Δ = b2-4ac
Δ = -122-4·2·(-19)
Δ = 296
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:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{74}}{2*2}=\frac{12-2\sqrt{74}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{74}}{2*2}=\frac{12+2\sqrt{74}}{4}
$