3/7x-6=2x+5

Solution for 3/7x-6=2x+5 equation:

3/7x-6=2x+5

We move all terms to the left:

3/7x-6-(2x+5)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

3/7x-2x-5-6=0

We multiply all the terms by the denominator


-2x*7x-5*7x-6*7x+3=0

Wy multiply elements

-14x^2-35x-42x+3=0

We add all the numbers together, and all the variables

-14x^2-77x+3=0

a = -14; b = -77; c = +3;
Δ = b2-4ac
Δ = -772-4·(-14)·3
Δ = 6097
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-\sqrt{6097}}{2*-14}=\frac{77-\sqrt{6097}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+\sqrt{6097}}{2*-14}=\frac{77+\sqrt{6097}}{-28}
$