19x^2=7-6x

Solution for 19x^2=7-6x equation:

19x^2=7-6x

We move all terms to the left:

19x^2-(7-6x)=0

We add all the numbers together, and all the variables

19x^2-(-6x+7)=0

We get rid of parentheses

19x^2+6x-7=0

a = 19; b = 6; c = -7;
Δ = b2-4ac
Δ = 62-4·19·(-7)
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{142}}{2*19}=\frac{-6-2\sqrt{142}}{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{142}}{2*19}=\frac{-6+2\sqrt{142}}{38}
$