5x+3=-7x+6+3/7x

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

5x+3=-7x+6+3/7x

We move all terms to the left:

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


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

35x^2+49x^2-42x+21x-3=0

We add all the numbers together, and all the variables

84x^2-21x-3=0

a = 84; b = -21; c = -3;
Δ = b2-4ac
Δ = -212-4·84·(-3)
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{161}}{2*84}=\frac{21-3\sqrt{161}}{168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{161}}{2*84}=\frac{21+3\sqrt{161}}{168}
$