5/8x+1/5x=55

Solution for 5/8x+1/5x=55 equation:

5/8x+1/5x=55

We move all terms to the left:

5/8x+1/5x-(55)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


25x/40x^2+8x/40x^2-55=0

We multiply all the terms by the denominator


25x+8x-55*40x^2=0

We add all the numbers together, and all the variables

33x-55*40x^2=0

Wy multiply elements

-2200x^2+33x=0

a = -2200; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·(-2200)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*-2200}=\frac{-66}{-4400}
=3/200
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*-2200}=\frac{0}{-4400}
=0
$