8/5x+3/4x=47/40

Solution for 8/5x+3/4x=47/40 equation:

8/5x+3/4x=47/40

We move all terms to the left:

8/5x+3/4x-(47/40)=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 add all the numbers together, and all the variables

8/5x+3/4x-(+47/40)=0

We get rid of parentheses

8/5x+3/4x-47/40=0

We calculate fractions


(-3760x^2)/3200x^2+5120x/3200x^2+2400x/3200x^2=0

We multiply all the terms by the denominator


(-3760x^2)+5120x+2400x=0

We add all the numbers together, and all the variables

(-3760x^2)+7520x=0

We get rid of parentheses

-3760x^2+7520x=0

a = -3760; b = 7520; c = 0;
Δ = b2-4ac
Δ = 75202-4·(-3760)·0
Δ = 56550400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{56550400}=7520$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7520)-7520}{2*-3760}=\frac{-15040}{-7520}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7520)+7520}{2*-3760}=\frac{0}{-7520}
=0
$