r(5r-14)=6

Solution for r(5r-14)=6 equation:

r(5r-14)=6

We move all terms to the left:

r(5r-14)-(6)=0

We multiply parentheses

5r^2-14r-6=0

a = 5; b = -14; c = -6;
Δ = b2-4ac
Δ = -142-4·5·(-6)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{79}}{2*5}=\frac{14-2\sqrt{79}}{10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{79}}{2*5}=\frac{14+2\sqrt{79}}{10}
$