12x^2=21-19x

Solution for 12x^2=21-19x equation:

12x^2=21-19x

We move all terms to the left:

12x^2-(21-19x)=0

We add all the numbers together, and all the variables

12x^2-(-19x+21)=0

We get rid of parentheses

12x^2+19x-21=0

a = 12; b = 19; c = -21;
Δ = b2-4ac
Δ = 192-4·12·(-21)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-37}{2*12}=\frac{-56}{24}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+37}{2*12}=\frac{18}{24}
=3/4
$