1/2x+2/5x=90

Solution for 1/2x+2/5x=90 equation:

1/2x+2/5x=90

We move all terms to the left:

1/2x+2/5x-(90)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


5x/10x^2+4x/10x^2-90=0

We multiply all the terms by the denominator


5x+4x-90*10x^2=0

We add all the numbers together, and all the variables

9x-90*10x^2=0

Wy multiply elements

-900x^2+9x=0

a = -900; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-900)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-900}=\frac{-18}{-1800}
=1/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-900}=\frac{0}{-1800}
=0
$