Y=2t-3/t+5

Solution for Y=2t-3/t+5 equation:

=2Y-3/Y+5

We move all terms to the left:

-(2Y-3/Y+5)=0


Domain of the equation: Y+5)!=0

Y∈R


We get rid of parentheses

-2Y+3/Y-5=0

We multiply all the terms by the denominator


-2Y*Y-5*Y+3=0

We add all the numbers together, and all the variables

-5Y-2Y*Y+3=0

Wy multiply elements

-2Y^2-5Y+3=0

a = -2; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·(-2)·3
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*-2}=\frac{-2}{-4}
=1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*-2}=\frac{12}{-4}
=-3
$