3x^2-6=-7x^-1

Solution for 3x^2-6=-7x^-1 equation:

3x^2-6=-7x^-1

We move all terms to the left:

3x^2-6-(-7x^-1)=0

We get rid of parentheses

3x^2+7x^+1-6=0

We add all the numbers together, and all the variables

3x^2+7x-5=0

a = 3; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·3·(-5)
Δ = 109
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{-(7)-\sqrt{109}}{2*3}=\frac{-7-\sqrt{109}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{109}}{2*3}=\frac{-7+\sqrt{109}}{6}
$