2/9x+5=7/6x-10

Solution for 2/9x+5=7/6x-10 equation:

2/9x+5=7/6x-10

We move all terms to the left:

2/9x+5-(7/6x-10)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 6x-10)!=0

x∈R


We get rid of parentheses

2/9x-7/6x+10+5=0

We calculate fractions


12x/54x^2+(-63x)/54x^2+10+5=0

We add all the numbers together, and all the variables

12x/54x^2+(-63x)/54x^2+15=0

We multiply all the terms by the denominator


12x+(-63x)+15*54x^2=0

Wy multiply elements

810x^2+12x+(-63x)=0

We get rid of parentheses

810x^2+12x-63x=0

We add all the numbers together, and all the variables

810x^2-51x=0

a = 810; b = -51; c = 0;
Δ = b2-4ac
Δ = -512-4·810·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-51}{2*810}=\frac{0}{1620}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+51}{2*810}=\frac{102}{1620}
=17/270
$