1/45x+1/40x=1

Solution for 1/45x+1/40x=1 equation:

1/45x+1/40x=1

We move all terms to the left:

1/45x+1/40x-(1)=0


Domain of the equation: 45x!=0

x!=0/45

x!=0

x∈R



Domain of the equation: 40x!=0

x!=0/40

x!=0

x∈R


We calculate fractions


40x/1800x^2+45x/1800x^2-1=0

We multiply all the terms by the denominator


40x+45x-1*1800x^2=0

We add all the numbers together, and all the variables

85x-1*1800x^2=0

Wy multiply elements

-1800x^2+85x=0

a = -1800; b = 85; c = 0;
Δ = b2-4ac
Δ = 852-4·(-1800)·0
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-85}{2*-1800}=\frac{-170}{-3600}
=17/360
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+85}{2*-1800}=\frac{0}{-3600}
=0
$