19x-12=4x^2

Solution for 19x-12=4x^2 equation:

19x-12=4x^2

We move all terms to the left:

19x-12-(4x^2)=0

determiningTheFunctionDomain
-4x^2+19x-12=0

a = -4; b = 19; c = -12;
Δ = b2-4ac
Δ = 192-4·(-4)·(-12)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-13}{2*-4}=\frac{-32}{-8}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+13}{2*-4}=\frac{-6}{-8}
=3/4
$