w2+6w=5/4

Solution for w2+6w=5/4 equation:

w2+6w=5/4

We move all terms to the left:

w2+6w-(5/4)=0

We add all the numbers together, and all the variables

w2+6w-(+5/4)=0

We add all the numbers together, and all the variables

w^2+6w-(+5/4)=0

We get rid of parentheses

w^2+6w-5/4=0

We multiply all the terms by the denominator


w^2*4+6w*4-5=0

Wy multiply elements

4w^2+24w-5=0

a = 4; b = 24; c = -5;
Δ = b2-4ac
Δ = 242-4·4·(-5)
Δ = 656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{41}}{2*4}=\frac{-24-4\sqrt{41}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{41}}{2*4}=\frac{-24+4\sqrt{41}}{8}
$