4y-1/2y=14

Solution for 4y-1/2y=14 equation:

4y-1/2y=14

We move all terms to the left:

4y-1/2y-(14)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We multiply all the terms by the denominator


4y*2y-14*2y-1=0

Wy multiply elements

8y^2-28y-1=0

a = 8; b = -28; c = -1;
Δ = b2-4ac
Δ = -282-4·8·(-1)
Δ = 816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{51}}{2*8}=\frac{28-4\sqrt{51}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{51}}{2*8}=\frac{28+4\sqrt{51}}{16}
$