5/4y+8=17.50;y=

Solution for 5/4y+8=17.50;y= equation:

5/4y+8=17.50y=

We move all terms to the left:

5/4y+8-(17.50y)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

5/4y-(+17.50y)+8=0

We get rid of parentheses

5/4y-17.50y+8=0

We multiply all the terms by the denominator


-(17.50y)*4y+8*4y+5=0

We add all the numbers together, and all the variables

-(+17.50y)*4y+8*4y+5=0

We multiply parentheses

-68y^2+8*4y+5=0

Wy multiply elements

-68y^2+32y+5=0

a = -68; b = 32; c = +5;
Δ = b2-4ac
Δ = 322-4·(-68)·5
Δ = 2384
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:

$\sqrt{\Delta}=\sqrt{2384}=\sqrt{16*149}=\sqrt{16}*\sqrt{149}=4\sqrt{149}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{149}}{2*-68}=\frac{-32-4\sqrt{149}}{-136}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{149}}{2*-68}=\frac{-32+4\sqrt{149}}{-136}
$