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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply parentheses

1/2x+2x-10-10=0

We multiply all the terms by the denominator


2x*2x-10*2x-10*2x+1=0

Wy multiply elements

4x^2-20x-20x+1=0

We add all the numbers together, and all the variables

4x^2-40x+1=0

a = 4; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·4·1
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-12\sqrt{11}}{2*4}=\frac{40-12\sqrt{11}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+12\sqrt{11}}{2*4}=\frac{40+12\sqrt{11}}{8}
$