Y=3x-2/2x+5

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

=3Y-2/2Y+5

We move all terms to the left:

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


Domain of the equation: 2Y+5)!=0

Y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6Y^2-10Y+2=0

a = -6; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·(-6)·2
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{37}}{2*-6}=\frac{10-2\sqrt{37}}{-12}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{37}}{2*-6}=\frac{10+2\sqrt{37}}{-12}
$