1/33x+4=x-2

Solution for 1/33x+4=x-2 equation:

1/33x+4=x-2

We move all terms to the left:

1/33x+4-(x-2)=0


Domain of the equation: 33x!=0

x!=0/33

x!=0

x∈R


We get rid of parentheses

1/33x-x+2+4=0

We multiply all the terms by the denominator


-x*33x+2*33x+4*33x+1=0

Wy multiply elements

-33x^2+66x+132x+1=0

We add all the numbers together, and all the variables

-33x^2+198x+1=0

a = -33; b = 198; c = +1;
Δ = b2-4ac
Δ = 1982-4·(-33)·1
Δ = 39336
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:

$\sqrt{\Delta}=\sqrt{39336}=\sqrt{4*9834}=\sqrt{4}*\sqrt{9834}=2\sqrt{9834}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(198)-2\sqrt{9834}}{2*-33}=\frac{-198-2\sqrt{9834}}{-66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(198)+2\sqrt{9834}}{2*-33}=\frac{-198+2\sqrt{9834}}{-66}
$