15x-14=10/9x

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Solution for 15x-14=10/9x equation: 



15x-14=10/9x

We move all terms to the left:

15x-14-(10/9x)=0



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R



We add all the numbers together, and all the variables

15x-(+10/9x)-14=0

We get rid of parentheses

15x-10/9x-14=0

We multiply all the terms by the denominator


15x*9x-14*9x-10=0

Wy multiply elements

135x^2-126x-10=0

a = 135; b = -126; c = -10;
Δ = b2-4ac
Δ = -1262-4·135·(-10)
Δ = 21276
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:


$\sqrt{\Delta}=\sqrt{21276}=\sqrt{36*591}=\sqrt{36}*\sqrt{591}=6\sqrt{591}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-6\sqrt{591}}{2*135}=\frac{126-6\sqrt{591}}{270}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+6\sqrt{591}}{2*135}=\frac{126+6\sqrt{591}}{270}
$

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