2r^2-26=9r

Solution for 2r^2-26=9r equation:

2r^2-26=9r

We move all terms to the left:

2r^2-26-(9r)=0

a = 2; b = -9; c = -26;
Δ = b2-4ac
Δ = -92-4·2·(-26)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-17}{2*2}=\frac{-8}{4}
=-2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+17}{2*2}=\frac{26}{4}
=6+1/2
$