-5/10x=8x+9

Solution for -5/10x=8x+9 equation:

-5/10x=8x+9

We move all terms to the left:

-5/10x-(8x+9)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We get rid of parentheses

-5/10x-8x-9=0

We multiply all the terms by the denominator


-8x*10x-9*10x-5=0

Wy multiply elements

-80x^2-90x-5=0

a = -80; b = -90; c = -5;
Δ = b2-4ac
Δ = -902-4·(-80)·(-5)
Δ = 6500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6500}=\sqrt{100*65}=\sqrt{100}*\sqrt{65}=10\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-10\sqrt{65}}{2*-80}=\frac{90-10\sqrt{65}}{-160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+10\sqrt{65}}{2*-80}=\frac{90+10\sqrt{65}}{-160}
$