4/9x+10/18x=61

Solution for 4/9x+10/18x=61 equation:

4/9x+10/18x=61

We move all terms to the left:

4/9x+10/18x-(61)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 18x!=0

x!=0/18

x!=0

x∈R


We calculate fractions


72x/162x^2+90x/162x^2-61=0

We multiply all the terms by the denominator


72x+90x-61*162x^2=0

We add all the numbers together, and all the variables

162x-61*162x^2=0

Wy multiply elements

-9882x^2+162x=0

a = -9882; b = 162; c = 0;
Δ = b2-4ac
Δ = 1622-4·(-9882)·0
Δ = 26244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{26244}=162$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(162)-162}{2*-9882}=\frac{-324}{-19764}
=1/61
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(162)+162}{2*-9882}=\frac{0}{-19764}
=0
$