3/2X-3/4y=5

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

3/2X-3/4X=5

We move all terms to the left:

3/2X-3/4X-(5)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R



Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We calculate fractions


12X/8X^2+(-6X)/8X^2-5=0

We multiply all the terms by the denominator


12X+(-6X)-5*8X^2=0

Wy multiply elements

-40X^2+12X+(-6X)=0

We get rid of parentheses

-40X^2+12X-6X=0

We add all the numbers together, and all the variables

-40X^2+6X=0

a = -40; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-40)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-40}=\frac{-12}{-80}
=3/20
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-40}=\frac{0}{-80}
=0
$