x2/6x+5=-8

Solution for x2/6x+5=-8 equation:

x2/6x+5=-8

We move all terms to the left:

x2/6x+5-(-8)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

x2/6x+13=0

We multiply all the terms by the denominator


x2+13*6x=0

We add all the numbers together, and all the variables

x^2+13*6x=0

Wy multiply elements

x^2+78x=0

a = 1; b = 78; c = 0;
Δ = b2-4ac
Δ = 782-4·1·0
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-78}{2*1}=\frac{-156}{2}
=-78
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+78}{2*1}=\frac{0}{2}
=0
$