2x+1=8/9x+10

Solution for 2x+1=8/9x+10 equation:

2x+1=8/9x+10

We move all terms to the left:

2x+1-(8/9x+10)=0


Domain of the equation: 9x+10)!=0

x∈R


We get rid of parentheses

2x-8/9x-10+1=0

We multiply all the terms by the denominator


2x*9x-10*9x+1*9x-8=0

Wy multiply elements

18x^2-90x+9x-8=0

We add all the numbers together, and all the variables

18x^2-81x-8=0

a = 18; b = -81; c = -8;
Δ = b2-4ac
Δ = -812-4·18·(-8)
Δ = 7137
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:

$\sqrt{\Delta}=\sqrt{7137}=\sqrt{9*793}=\sqrt{9}*\sqrt{793}=3\sqrt{793}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-3\sqrt{793}}{2*18}=\frac{81-3\sqrt{793}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+3\sqrt{793}}{2*18}=\frac{81+3\sqrt{793}}{36}
$