2w^2-13w=-21

Solution for 2w^2-13w=-21 equation:

2w^2-13w=-21

We move all terms to the left:

2w^2-13w-(-21)=0

We add all the numbers together, and all the variables

2w^2-13w+21=0

a = 2; b = -13; c = +21;
Δ = b2-4ac
Δ = -132-4·2·21
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-1}{2*2}=\frac{12}{4}
=3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+1}{2*2}=\frac{14}{4}
=3+1/2
$