1/2x+7=3+x-10

Solution for 1/2x+7=3+x-10 equation:

1/2x+7=3+x-10

We move all terms to the left:

1/2x+7-(3+x-10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(x-7)+7=0

We get rid of parentheses

1/2x-x+7+7=0

We multiply all the terms by the denominator


-x*2x+7*2x+7*2x+1=0

Wy multiply elements

-2x^2+14x+14x+1=0

We add all the numbers together, and all the variables

-2x^2+28x+1=0

a = -2; b = 28; c = +1;
Δ = b2-4ac
Δ = 282-4·(-2)·1
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-6\sqrt{22}}{2*-2}=\frac{-28-6\sqrt{22}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+6\sqrt{22}}{2*-2}=\frac{-28+6\sqrt{22}}{-4}
$