2x+10=2000/27x+7

Solution for 2x+10=2000/27x+7 equation:

2x+10=2000/27x+7

We move all terms to the left:

2x+10-(2000/27x+7)=0


Domain of the equation: 27x+7)!=0

x∈R


We get rid of parentheses

2x-2000/27x-7+10=0

We multiply all the terms by the denominator


2x*27x-7*27x+10*27x-2000=0

Wy multiply elements

54x^2-189x+270x-2000=0

We add all the numbers together, and all the variables

54x^2+81x-2000=0

a = 54; b = 81; c = -2000;
Δ = b2-4ac
Δ = 812-4·54·(-2000)
Δ = 438561
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:

$\sqrt{\Delta}=\sqrt{438561}=\sqrt{9*48729}=\sqrt{9}*\sqrt{48729}=3\sqrt{48729}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-3\sqrt{48729}}{2*54}=\frac{-81-3\sqrt{48729}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+3\sqrt{48729}}{2*54}=\frac{-81+3\sqrt{48729}}{108}
$