1/45x+1/50x=38

Solution for 1/45x+1/50x=38 equation:

1/45x+1/50x=38

We move all terms to the left:

1/45x+1/50x-(38)=0


Domain of the equation: 45x!=0

x!=0/45

x!=0

x∈R



Domain of the equation: 50x!=0

x!=0/50

x!=0

x∈R


We calculate fractions


50x/2250x^2+45x/2250x^2-38=0

We multiply all the terms by the denominator


50x+45x-38*2250x^2=0

We add all the numbers together, and all the variables

95x-38*2250x^2=0

Wy multiply elements

-85500x^2+95x=0

a = -85500; b = 95; c = 0;
Δ = b2-4ac
Δ = 952-4·(-85500)·0
Δ = 9025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9025}=95$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(95)-95}{2*-85500}=\frac{-190}{-171000}
=1/900
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(95)+95}{2*-85500}=\frac{0}{-171000}
=0
$