2b^2+9b=26

Solution for 2b^2+9b=26 equation:

2b^2+9b=26

We move all terms to the left:

2b^2+9b-(26)=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:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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