x-12=1/2x+7

Solution for x-12=1/2x+7 equation:

x-12=1/2x+7

We move all terms to the left:

x-12-(1/2x+7)=0


Domain of the equation: 2x+7)!=0

x∈R


We get rid of parentheses

x-1/2x-7-12=0

We multiply all the terms by the denominator


x*2x-7*2x-12*2x-1=0

Wy multiply elements

2x^2-14x-24x-1=0

We add all the numbers together, and all the variables

2x^2-38x-1=0

a = 2; b = -38; c = -1;
Δ = b2-4ac
Δ = -382-4·2·(-1)
Δ = 1452
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:

$\sqrt{\Delta}=\sqrt{1452}=\sqrt{484*3}=\sqrt{484}*\sqrt{3}=22\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-22\sqrt{3}}{2*2}=\frac{38-22\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+22\sqrt{3}}{2*2}=\frac{38+22\sqrt{3}}{4}
$