(2x+20)/2x=5x-4

Solution for (2x+20)/2x=5x-4 equation:

(2x+20)/2x=5x-4

We move all terms to the left:

(2x+20)/2x-(5x-4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

(2x+20)/2x-5x+4=0

We multiply all the terms by the denominator


(2x+20)-5x*2x+4*2x=0

Wy multiply elements

-10x^2+(2x+20)+8x=0

We get rid of parentheses

-10x^2+2x+8x+20=0

We add all the numbers together, and all the variables

-10x^2+10x+20=0

a = -10; b = 10; c = +20;
Δ = b2-4ac
Δ = 102-4·(-10)·20
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-30}{2*-10}=\frac{-40}{-20}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+30}{2*-10}=\frac{20}{-20}
=-1
$