7x+2/3x=92

Solution for 7x+2/3x=92 equation:

7x+2/3x=92

We move all terms to the left:

7x+2/3x-(92)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


7x*3x-92*3x+2=0

Wy multiply elements

21x^2-276x+2=0

a = 21; b = -276; c = +2;
Δ = b2-4ac
Δ = -2762-4·21·2
Δ = 76008
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:

$\sqrt{\Delta}=\sqrt{76008}=\sqrt{4*19002}=\sqrt{4}*\sqrt{19002}=2\sqrt{19002}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-276)-2\sqrt{19002}}{2*21}=\frac{276-2\sqrt{19002}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-276)+2\sqrt{19002}}{2*21}=\frac{276+2\sqrt{19002}}{42}
$