(5x^2-3x-8)/(x+5)=0

Solution for (5x^2-3x-8)/(x+5)=0 equation:

(5x^2-3x-8)/(x+5)=0


Domain of the equation: (x+5)!=0

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

x!=-5

x∈R


We multiply all the terms by the denominator


(5x^2-3x-8)=0

We get rid of parentheses

5x^2-3x-8=0

a = 5; b = -3; c = -8;
Δ = b2-4ac
Δ = -32-4·5·(-8)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-13}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+13}{2*5}=\frac{16}{10}
=1+3/5
$