7x^2+2x=19

Solution for 7x^2+2x=19 equation:

7x^2+2x=19

We move all terms to the left:

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

a = 7; b = 2; c = -19;
Δ = b2-4ac
Δ = 22-4·7·(-19)
Δ = 536
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:

$\sqrt{\Delta}=\sqrt{536}=\sqrt{4*134}=\sqrt{4}*\sqrt{134}=2\sqrt{134}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{134}}{2*7}=\frac{-2-2\sqrt{134}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{134}}{2*7}=\frac{-2+2\sqrt{134}}{14}
$