y-7/8y=22

Solution for y-7/8y=22 equation:

y-7/8y=22

We move all terms to the left:

y-7/8y-(22)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We multiply all the terms by the denominator


y*8y-22*8y-7=0

Wy multiply elements

8y^2-176y-7=0

a = 8; b = -176; c = -7;
Δ = b2-4ac
Δ = -1762-4·8·(-7)
Δ = 31200
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:

$\sqrt{\Delta}=\sqrt{31200}=\sqrt{400*78}=\sqrt{400}*\sqrt{78}=20\sqrt{78}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-20\sqrt{78}}{2*8}=\frac{176-20\sqrt{78}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+20\sqrt{78}}{2*8}=\frac{176+20\sqrt{78}}{16}
$