6r2+11r-19=5

Solution for 6r2+11r-19=5 equation:

6r^2+11r-19=5

We move all terms to the left:

6r^2+11r-19-(5)=0

We add all the numbers together, and all the variables

6r^2+11r-24=0

a = 6; b = 11; c = -24;
Δ = b2-4ac
Δ = 112-4·6·(-24)
Δ = 697
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{-(11)-\sqrt{697}}{2*6}=\frac{-11-\sqrt{697}}{12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{697}}{2*6}=\frac{-11+\sqrt{697}}{12}
$