7x+8/3x=12

Solution for 7x+8/3x=12 equation:

7x+8/3x=12

We move all terms to the left:

7x+8/3x-(12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


7x*3x-12*3x+8=0

Wy multiply elements

21x^2-36x+8=0

a = 21; b = -36; c = +8;
Δ = b2-4ac
Δ = -362-4·21·8
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{39}}{2*21}=\frac{36-4\sqrt{39}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{39}}{2*21}=\frac{36+4\sqrt{39}}{42}
$