y=4/2y-3=3/5

Solution for y=4/2y-3=3/5 equation:

y=4/2y-3=3/5

We move all terms to the left:

y-(4/2y-3)=0


Domain of the equation: 2y-3)!=0

y∈R


We get rid of parentheses

y-4/2y+3=0

We multiply all the terms by the denominator


y*2y+3*2y-4=0

Wy multiply elements

2y^2+6y-4=0

a = 2; b = 6; c = -4;
Δ = b2-4ac
Δ = 62-4·2·(-4)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{17}}{2*2}=\frac{-6-2\sqrt{17}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{17}}{2*2}=\frac{-6+2\sqrt{17}}{4}
$