7/x+3-3(x+8)=4

Solution for 7/x+3-3(x+8)=4 equation:

7/x+3-3(x+8)=4

We move all terms to the left:

7/x+3-3(x+8)-(4)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

7/x-3(x+8)-1=0

We multiply parentheses

7/x-3x-24-1=0

We multiply all the terms by the denominator


-3x*x-24*x-1*x+7=0

We add all the numbers together, and all the variables

-25x-3x*x+7=0

Wy multiply elements

-3x^2-25x+7=0

a = -3; b = -25; c = +7;
Δ = b2-4ac
Δ = -252-4·(-3)·7
Δ = 709
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-\sqrt{709}}{2*-3}=\frac{25-\sqrt{709}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{709}}{2*-3}=\frac{25+\sqrt{709}}{-6}
$