w+14/4w=6=3/4

Solution for w+14/4w=6=3/4 equation:

w+14/4w=6=3/4

We move all terms to the left:

w+14/4w-(6)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R


We multiply all the terms by the denominator


w*4w-6*4w+14=0

Wy multiply elements

4w^2-24w+14=0

a = 4; b = -24; c = +14;
Δ = b2-4ac
Δ = -242-4·4·14
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{22}}{2*4}=\frac{24-4\sqrt{22}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{22}}{2*4}=\frac{24+4\sqrt{22}}{8}
$