2w2-13w=7

Solution for 2w2-13w=7 equation:

2w^2-13w=7

We move all terms to the left:

2w^2-13w-(7)=0

a = 2; b = -13; c = -7;
Δ = b2-4ac
Δ = -132-4·2·(-7)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-15}{2*2}=\frac{-2}{4}
=-1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+15}{2*2}=\frac{28}{4}
=7
$