y-5/8y=3

Solution for y-5/8y=3 equation:

y-5/8y=3

We move all terms to the left:

y-5/8y-(3)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We multiply all the terms by the denominator


y*8y-3*8y-5=0

Wy multiply elements

8y^2-24y-5=0

a = 8; b = -24; c = -5;
Δ = b2-4ac
Δ = -242-4·8·(-5)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{46}}{2*8}=\frac{24-4\sqrt{46}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{46}}{2*8}=\frac{24+4\sqrt{46}}{16}
$