2w^2-5w=273

Solution for 2w^2-5w=273 equation:

2w^2-5w=273

We move all terms to the left:

2w^2-5w-(273)=0

a = 2; b = -5; c = -273;
Δ = b2-4ac
Δ = -52-4·2·(-273)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-47}{2*2}=\frac{-42}{4}
=-10+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+47}{2*2}=\frac{52}{4}
=13
$