-10=1/2*x+x

Solution for -10=1/2*x+x equation:

-10=1/2x+x

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-x-1/2x-10=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -2; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·(-2)·(-1)
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-14\sqrt{2}}{2*-2}=\frac{20-14\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+14\sqrt{2}}{2*-2}=\frac{20+14\sqrt{2}}{-4}
$