19x=7-6x^2

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

19x=7-6x^2

We move all terms to the left:

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

We get rid of parentheses

6x^2+19x-7=0

a = 6; b = 19; c = -7;
Δ = b2-4ac
Δ = 192-4·6·(-7)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-23}{2*6}=\frac{-42}{12}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+23}{2*6}=\frac{4}{12}
=1/3
$