7x-2=1/3x+5

Solution for 7x-2=1/3x+5 equation:

7x-2=1/3x+5

We move all terms to the left:

7x-2-(1/3x+5)=0


Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

7x-1/3x-5-2=0

We multiply all the terms by the denominator


7x*3x-5*3x-2*3x-1=0

Wy multiply elements

21x^2-15x-6x-1=0

We add all the numbers together, and all the variables

21x^2-21x-1=0

a = 21; b = -21; c = -1;
Δ = b2-4ac
Δ = -212-4·21·(-1)
Δ = 525
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:

$\sqrt{\Delta}=\sqrt{525}=\sqrt{25*21}=\sqrt{25}*\sqrt{21}=5\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-5\sqrt{21}}{2*21}=\frac{21-5\sqrt{21}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+5\sqrt{21}}{2*21}=\frac{21+5\sqrt{21}}{42}
$