X+23=1/2x+7

Solution for X+23=1/2x+7 equation:

X+23=1/2X+7

We move all terms to the left:

X+23-(1/2X+7)=0


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

X∈R


We get rid of parentheses

X-1/2X-7+23=0

We multiply all the terms by the denominator


X*2X-7*2X+23*2X-1=0

Wy multiply elements

2X^2-14X+46X-1=0

We add all the numbers together, and all the variables

2X^2+32X-1=0

a = 2; b = 32; c = -1;
Δ = b2-4ac
Δ = 322-4·2·(-1)
Δ = 1032
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:

$\sqrt{\Delta}=\sqrt{1032}=\sqrt{4*258}=\sqrt{4}*\sqrt{258}=2\sqrt{258}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{258}}{2*2}=\frac{-32-2\sqrt{258}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{258}}{2*2}=\frac{-32+2\sqrt{258}}{4}
$