7p^2-14p=19

Solution for 7p^2-14p=19 equation:

7p^2-14p=19

We move all terms to the left:

7p^2-14p-(19)=0

a = 7; b = -14; c = -19;
Δ = b2-4ac
Δ = -142-4·7·(-19)
Δ = 728
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{728}=\sqrt{4*182}=\sqrt{4}*\sqrt{182}=2\sqrt{182}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{182}}{2*7}=\frac{14-2\sqrt{182}}{14}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{182}}{2*7}=\frac{14+2\sqrt{182}}{14}
$