2x^2=19x+14

Solution for 2x^2=19x+14 equation:

2x^2=19x+14

We move all terms to the left:

2x^2-(19x+14)=0

We get rid of parentheses

2x^2-19x-14=0

a = 2; b = -19; c = -14;
Δ = b2-4ac
Δ = -192-4·2·(-14)
Δ = 473
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{473}}{2*2}=\frac{19-\sqrt{473}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{473}}{2*2}=\frac{19+\sqrt{473}}{4}
$