X/5x+2=4x-9

Solution for X/5x+2=4x-9 equation:

X/5X+2=4X-9

We move all terms to the left:

X/5X+2-(4X-9)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We get rid of parentheses

X/5X-4X+9+2=0

We multiply all the terms by the denominator


X-4X*5X+9*5X+2*5X=0

Wy multiply elements

-20X^2+X+45X+10X=0

We add all the numbers together, and all the variables

-20X^2+56X=0

a = -20; b = 56; c = 0;
Δ = b2-4ac
Δ = 562-4·(-20)·0
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-56}{2*-20}=\frac{-112}{-40}
=2+4/5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+56}{2*-20}=\frac{0}{-40}
=0
$