x+72=1/2*x+15

Solution for x+72=1/2*x+15 equation:

x+72=1/2x+15

We move all terms to the left:

x+72-(1/2x+15)=0


Domain of the equation: 2x+15)!=0

x∈R


We get rid of parentheses

x-1/2x-15+72=0

We multiply all the terms by the denominator


x*2x-15*2x+72*2x-1=0

Wy multiply elements

2x^2-30x+144x-1=0

We add all the numbers together, and all the variables

2x^2+114x-1=0

a = 2; b = 114; c = -1;
Δ = b2-4ac
Δ = 1142-4·2·(-1)
Δ = 13004
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:

$\sqrt{\Delta}=\sqrt{13004}=\sqrt{4*3251}=\sqrt{4}*\sqrt{3251}=2\sqrt{3251}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(114)-2\sqrt{3251}}{2*2}=\frac{-114-2\sqrt{3251}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+2\sqrt{3251}}{2*2}=\frac{-114+2\sqrt{3251}}{4}
$