3/5X+1/4y=-1/2

Solution for 3/5X+1/4y=-1/2 equation:

3/5X+1/4X=-1/2

We move all terms to the left:

3/5X+1/4X-(-1/2)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R



Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We get rid of parentheses

3/5X+1/4X+1/2=0

We calculate fractions


80X^2/80X^2+48X/80X^2+20X/80X^2=0

Fractions to decimals

48X/80X^2+20X/80X^2+1=0

We multiply all the terms by the denominator


48X+20X+1*80X^2=0

We add all the numbers together, and all the variables

68X+1*80X^2=0

Wy multiply elements

80X^2+68X=0

a = 80; b = 68; c = 0;
Δ = b2-4ac
Δ = 682-4·80·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-68}{2*80}=\frac{-136}{160}
=-17/20
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+68}{2*80}=\frac{0}{160}
=0
$