1/30x+1/75x=1

Solution for 1/30x+1/75x=1 equation:

1/30x+1/75x=1

We move all terms to the left:

1/30x+1/75x-(1)=0


Domain of the equation: 30x!=0

x!=0/30

x!=0

x∈R



Domain of the equation: 75x!=0

x!=0/75

x!=0

x∈R


We calculate fractions


75x/2250x^2+30x/2250x^2-1=0

We multiply all the terms by the denominator


75x+30x-1*2250x^2=0

We add all the numbers together, and all the variables

105x-1*2250x^2=0

Wy multiply elements

-2250x^2+105x=0

a = -2250; b = 105; c = 0;
Δ = b2-4ac
Δ = 1052-4·(-2250)·0
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-105}{2*-2250}=\frac{-210}{-4500}
=7/150
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+105}{2*-2250}=\frac{0}{-4500}
=0
$