2x^2-19x=100

Solution for 2x^2-19x=100 equation:

2x^2-19x=100

We move all terms to the left:

2x^2-19x-(100)=0

a = 2; b = -19; c = -100;
Δ = b2-4ac
Δ = -192-4·2·(-100)
Δ = 1161
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:

$\sqrt{\Delta}=\sqrt{1161}=\sqrt{9*129}=\sqrt{9}*\sqrt{129}=3\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-3\sqrt{129}}{2*2}=\frac{19-3\sqrt{129}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+3\sqrt{129}}{2*2}=\frac{19+3\sqrt{129}}{4}
$