7r^2-12r=17

Solution for 7r^2-12r=17 equation:

7r^2-12r=17

We move all terms to the left:

7r^2-12r-(17)=0

a = 7; b = -12; c = -17;
Δ = b2-4ac
Δ = -122-4·7·(-17)
Δ = 620
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{620}=\sqrt{4*155}=\sqrt{4}*\sqrt{155}=2\sqrt{155}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{155}}{2*7}=\frac{12-2\sqrt{155}}{14}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{155}}{2*7}=\frac{12+2\sqrt{155}}{14}
$