x/40x=20x+120

Solution for x/40x=20x+120 equation:

x/40x=20x+120

We move all terms to the left:

x/40x-(20x+120)=0


Domain of the equation: 40x!=0

x!=0/40

x!=0

x∈R


We get rid of parentheses

x/40x-20x-120=0

We multiply all the terms by the denominator


x-20x*40x-120*40x=0

Wy multiply elements

-800x^2+x-4800x=0

We add all the numbers together, and all the variables

-800x^2-4799x=0

a = -800; b = -4799; c = 0;
Δ = b2-4ac
Δ = -47992-4·(-800)·0
Δ = 23030401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{23030401}=4799$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4799)-4799}{2*-800}=\frac{0}{-1600}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4799)+4799}{2*-800}=\frac{9598}{-1600}
=-5+799/800
$