7r^2-5r=19

Solution for 7r^2-5r=19 equation:

7r^2-5r=19

We move all terms to the left:

7r^2-5r-(19)=0

a = 7; b = -5; c = -19;
Δ = b2-4ac
Δ = -52-4·7·(-19)
Δ = 557
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{557}}{2*7}=\frac{5-\sqrt{557}}{14}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{557}}{2*7}=\frac{5+\sqrt{557}}{14}
$