(1/3-5)x=171

Solution for (1/3-5)x=171 equation:

(1/3-5)x=171

We move all terms to the left:

(1/3-5)x-(171)=0


Domain of the equation: 3-5)x!=0

We move all terms containing x to the left, all other terms to the right

-5)x!=-3

x!=-3/1

x!=-3

x∈R


We multiply parentheses

x^2-5x-171=0

a = 1; b = -5; c = -171;
Δ = b2-4ac
Δ = -52-4·1·(-171)
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{-(-5)-\sqrt{709}}{2*1}=\frac{5-\sqrt{709}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{709}}{2*1}=\frac{5+\sqrt{709}}{2}
$