7x+6=56/3x

Solution for 7x+6=56/3x equation:

7x+6=56/3x

We move all terms to the left:

7x+6-(56/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7x-(+56/3x)+6=0

We get rid of parentheses

7x-56/3x+6=0

We multiply all the terms by the denominator


7x*3x+6*3x-56=0

Wy multiply elements

21x^2+18x-56=0

a = 21; b = 18; c = -56;
Δ = b2-4ac
Δ = 182-4·21·(-56)
Δ = 5028
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:

$\sqrt{\Delta}=\sqrt{5028}=\sqrt{4*1257}=\sqrt{4}*\sqrt{1257}=2\sqrt{1257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{1257}}{2*21}=\frac{-18-2\sqrt{1257}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{1257}}{2*21}=\frac{-18+2\sqrt{1257}}{42}
$