10y-(3/2y)+8=7+6y-4.5

Solution for 10y-(3/2y)+8=7+6y-4.5 equation:

10y-(3/2y)+8=7+6y-4.5

We move all terms to the left:

10y-(3/2y)+8-(7+6y-4.5)=0


Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

10y-(+3/2y)-(6y+2.5)+8=0

We get rid of parentheses

10y-3/2y-6y-2.5+8=0

We multiply all the terms by the denominator


10y*2y-6y*2y-(2.5)*2y+8*2y-3=0

We multiply parentheses

10y*2y-6y*2y-5y+8*2y-3=0

Wy multiply elements

20y^2-12y^2-5y+16y-3=0

We add all the numbers together, and all the variables

8y^2+11y-3=0

a = 8; b = 11; c = -3;
Δ = b2-4ac
Δ = 112-4·8·(-3)
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{217}}{2*8}=\frac{-11-\sqrt{217}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{217}}{2*8}=\frac{-11+\sqrt{217}}{16}
$