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

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

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

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2+8x-20x+1=0

We add all the numbers together, and all the variables

2x^2-12x+1=0

a = 2; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·2·1
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{34}}{2*2}=\frac{12-2\sqrt{34}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{34}}{2*2}=\frac{12+2\sqrt{34}}{4}
$