10+x=5(1/2x+2)

Solution for 10+x=5(1/2x+2) equation:

10+x=5(1/2x+2)

We move all terms to the left:

10+x-(5(1/2x+2))=0


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

x∈R


We multiply all the terms by the denominator


x*2x+10*2x+2))-(5(1+2))=0

We add all the numbers together, and all the variables

x*2x+10*2x+2))-(53)=0

We add all the numbers together, and all the variables

x*2x+10*2x=0

Wy multiply elements

2x^2+20x=0

a = 2; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·2·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*2}=\frac{-40}{4}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*2}=\frac{0}{4}
=0
$