14/15x+21=11/5x+18

Solution for 14/15x+21=11/5x+18 equation:

14/15x+21=11/5x+18

We move all terms to the left:

14/15x+21-(11/5x+18)=0


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R



Domain of the equation: 5x+18)!=0

x∈R


We get rid of parentheses

14/15x-11/5x-18+21=0

We calculate fractions


70x/75x^2+(-165x)/75x^2-18+21=0

We add all the numbers together, and all the variables

70x/75x^2+(-165x)/75x^2+3=0

We multiply all the terms by the denominator


70x+(-165x)+3*75x^2=0

Wy multiply elements

225x^2+70x+(-165x)=0

We get rid of parentheses

225x^2+70x-165x=0

We add all the numbers together, and all the variables

225x^2-95x=0

a = 225; b = -95; c = 0;
Δ = b2-4ac
Δ = -952-4·225·0
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*225}=\frac{0}{450}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95)+95}{2*225}=\frac{190}{450}
=19/45
$