y-7/8y=5

Solution for y-7/8y=5 equation:

y-7/8y=5

We move all terms to the left:

y-7/8y-(5)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We multiply all the terms by the denominator


y*8y-5*8y-7=0

Wy multiply elements

8y^2-40y-7=0

a = 8; b = -40; c = -7;
Δ = b2-4ac
Δ = -402-4·8·(-7)
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{114}}{2*8}=\frac{40-4\sqrt{114}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{114}}{2*8}=\frac{40+4\sqrt{114}}{16}
$