10+x=4(1/4x+2)

Solution for 10+x=4(1/4x+2) equation:

10+x=4(1/4x+2)

We move all terms to the left:

10+x-(4(1/4x+2))=0


Domain of the equation: 4x+2))!=0

x∈R


We multiply all the terms by the denominator


x*4x+10*4x+2))-(4(1+2))=0

We add all the numbers together, and all the variables

x*4x+10*4x+2))-(43)=0

We add all the numbers together, and all the variables

x*4x+10*4x=0

Wy multiply elements

4x^2+40x=0

a = 4; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·4·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*4}=\frac{-80}{8}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*4}=\frac{0}{8}
=0
$