4/20x+10=2x-26

Solution for 4/20x+10=2x-26 equation:

4/20x+10=2x-26

We move all terms to the left:

4/20x+10-(2x-26)=0


Domain of the equation: 20x!=0

x!=0/20

x!=0

x∈R


We get rid of parentheses

4/20x-2x+26+10=0

We multiply all the terms by the denominator


-2x*20x+26*20x+10*20x+4=0

Wy multiply elements

-40x^2+520x+200x+4=0

We add all the numbers together, and all the variables

-40x^2+720x+4=0

a = -40; b = 720; c = +4;
Δ = b2-4ac
Δ = 7202-4·(-40)·4
Δ = 519040
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:

$\sqrt{\Delta}=\sqrt{519040}=\sqrt{64*8110}=\sqrt{64}*\sqrt{8110}=8\sqrt{8110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(720)-8\sqrt{8110}}{2*-40}=\frac{-720-8\sqrt{8110}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(720)+8\sqrt{8110}}{2*-40}=\frac{-720+8\sqrt{8110}}{-80}
$