x-4=1/2x+3

Solution for x-4=1/2x+3 equation:

x-4=1/2x+3

We move all terms to the left:

x-4-(1/2x+3)=0


Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

x-1/2x-3-4=0

We multiply all the terms by the denominator


x*2x-3*2x-4*2x-1=0

Wy multiply elements

2x^2-6x-8x-1=0

We add all the numbers together, and all the variables

2x^2-14x-1=0

a = 2; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·2·(-1)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{51}}{2*2}=\frac{14-2\sqrt{51}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{51}}{2*2}=\frac{14+2\sqrt{51}}{4}
$