19x-12=2x^2

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

19x-12=2x^2

We move all terms to the left:

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

determiningTheFunctionDomain
-2x^2+19x-12=0

a = -2; b = 19; c = -12;
Δ = b2-4ac
Δ = 192-4·(-2)·(-12)
Δ = 265
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{265}}{2*-2}=\frac{-19-\sqrt{265}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{265}}{2*-2}=\frac{-19+\sqrt{265}}{-4}
$