3/7x+3-x+3=12

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

3/7x+3-x+3=12

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/7x-6=0

We multiply all the terms by the denominator


-1x*7x-6*7x+3=0

Wy multiply elements

-7x^2-42x+3=0

a = -7; b = -42; c = +3;
Δ = b2-4ac
Δ = -422-4·(-7)·3
Δ = 1848
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:

$\sqrt{\Delta}=\sqrt{1848}=\sqrt{4*462}=\sqrt{4}*\sqrt{462}=2\sqrt{462}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{462}}{2*-7}=\frac{42-2\sqrt{462}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{462}}{2*-7}=\frac{42+2\sqrt{462}}{-14}
$