-10.2x-16=-24/5x

Solution for -10.2x-16=-24/5x equation:

-10.2x-16=-24/5x

We move all terms to the left:

-10.2x-16-(-24/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-10.2x+24/5x-16=0

We multiply all the terms by the denominator


-(10.2x)*5x-16*5x+24=0

We add all the numbers together, and all the variables

-(+10.2x)*5x-16*5x+24=0

We multiply parentheses

-50x^2-16*5x+24=0

Wy multiply elements

-50x^2-80x+24=0

a = -50; b = -80; c = +24;
Δ = b2-4ac
Δ = -802-4·(-50)·24
Δ = 11200
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:

$\sqrt{\Delta}=\sqrt{11200}=\sqrt{1600*7}=\sqrt{1600}*\sqrt{7}=40\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-40\sqrt{7}}{2*-50}=\frac{80-40\sqrt{7}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+40\sqrt{7}}{2*-50}=\frac{80+40\sqrt{7}}{-100}
$