7+7+0+9+9+9-0-9-46-2890+56+689+20-98+42X-3/3x=45-x-67-8X

Solution for 7+7+0+9+9+9-0-9-46-2890+56+689+20-98+42X-3/3x=45-x-67-8X equation:

7+7+0+9+9+9-0-9-46-2890+56+689+20-98+42X-3/3X=45-X-67-8X

We move all terms to the left:

7+7+0+9+9+9-0-9-46-2890+56+689+20-98+42X-3/3X-(45-X-67-8X)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

42X-3/3X-(-9X-22)+7+7+0+9+9+9-0-9-46-2890+56+689+20-98=0

We add all the numbers together, and all the variables

42X-3/3X-(-9X-22)-2237=0

We get rid of parentheses

42X-3/3X+9X+22-2237=0

We multiply all the terms by the denominator


42X*3X+9X*3X+22*3X-2237*3X-3=0

Wy multiply elements

126X^2+27X^2+66X-6711X-3=0

We add all the numbers together, and all the variables

153X^2-6645X-3=0

a = 153; b = -6645; c = -3;
Δ = b2-4ac
Δ = -66452-4·153·(-3)
Δ = 44157861
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:

$\sqrt{\Delta}=\sqrt{44157861}=\sqrt{1089*40549}=\sqrt{1089}*\sqrt{40549}=33\sqrt{40549}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6645)-33\sqrt{40549}}{2*153}=\frac{6645-33\sqrt{40549}}{306}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6645)+33\sqrt{40549}}{2*153}=\frac{6645+33\sqrt{40549}}{306}
$