1/2x+15=x-7

Solution for 1/2x+15=x-7 equation:

1/2x+15=x-7

We move all terms to the left:

1/2x+15-(x-7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-x+7+15=0

We multiply all the terms by the denominator


-x*2x+7*2x+15*2x+1=0

Wy multiply elements

-2x^2+14x+30x+1=0

We add all the numbers together, and all the variables

-2x^2+44x+1=0

a = -2; b = 44; c = +1;
Δ = b2-4ac
Δ = 442-4·(-2)·1
Δ = 1944
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:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-18\sqrt{6}}{2*-2}=\frac{-44-18\sqrt{6}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+18\sqrt{6}}{2*-2}=\frac{-44+18\sqrt{6}}{-4}
$