3x=7,-7/9x-42

Solution for 3x=7,-7/9x-42 equation:

3x=7.-7/9x-42

We move all terms to the left:

3x-(7.-7/9x-42)=0


Domain of the equation: 9x-42)!=0

x∈R


We add all the numbers together, and all the variables

3x-(-7/9x-35)=0

We get rid of parentheses

3x+7/9x+35=0

We multiply all the terms by the denominator


3x*9x+35*9x+7=0

Wy multiply elements

27x^2+315x+7=0

a = 27; b = 315; c = +7;
Δ = b2-4ac
Δ = 3152-4·27·7
Δ = 98469
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:

$\sqrt{\Delta}=\sqrt{98469}=\sqrt{9*10941}=\sqrt{9}*\sqrt{10941}=3\sqrt{10941}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(315)-3\sqrt{10941}}{2*27}=\frac{-315-3\sqrt{10941}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(315)+3\sqrt{10941}}{2*27}=\frac{-315+3\sqrt{10941}}{54}
$