5x/8x=-9x

Solution for 5x/8x=-9x equation:

5x/8x=-9x

We move all terms to the left:

5x/8x-(-9x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

5x/8x+9x=0

We multiply all the terms by the denominator


5x+9x*8x=0

Wy multiply elements

72x^2+5x=0

a = 72; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·72·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*72}=\frac{-10}{144}
=-5/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*72}=\frac{0}{144}
=0
$