0.7w+16/4w=27.28

Solution for 0.7w+16/4w=27.28 equation:

0.7w+16/4w=27.28

We move all terms to the left:

0.7w+16/4w-(27.28)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R


We add all the numbers together, and all the variables

0.7w+16/4w-27.28=0

We multiply all the terms by the denominator


(0.7w)*4w-(27.28)*4w+16=0

We add all the numbers together, and all the variables

(+0.7w)*4w-(27.28)*4w+16=0

We multiply parentheses

0w^2-109.12w+16=0

We add all the numbers together, and all the variables

w^2-109.12w+16=0

a = 1; b = -109.12; c = +16;
Δ = b2-4ac
Δ = -109.122-4·1·16
Δ = 11843.1744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-109.12)-\sqrt{11843.1744}}{2*1}=\frac{109.12-\sqrt{11843.1744}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-109.12)+\sqrt{11843.1744}}{2*1}=\frac{109.12+\sqrt{11843.1744}}{2}
$