7/x-8=3-x

Solution for 7/x-8=3-x equation:

7/x-8=3-x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


1x*x-3*x-8*x+7=0

We add all the numbers together, and all the variables

-11x+1x*x+7=0

Wy multiply elements

x^2-11x+7=0

a = 1; b = -11; c = +7;
Δ = b2-4ac
Δ = -112-4·1·7
Δ = 93
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{-(-11)-\sqrt{93}}{2*1}=\frac{11-\sqrt{93}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{93}}{2*1}=\frac{11+\sqrt{93}}{2}
$