(X-8)=-1/2x+7

Solution for (X-8)=-1/2x+7 equation:

(X-8)=-1/2X+7

We move all terms to the left:

(X-8)-(-1/2X+7)=0


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

X∈R


We get rid of parentheses

X+1/2X-8-7=0

We multiply all the terms by the denominator


X*2X-8*2X-7*2X+1=0

Wy multiply elements

2X^2-16X-14X+1=0

We add all the numbers together, and all the variables

2X^2-30X+1=0

a = 2; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·2·1
Δ = 892
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:

$\sqrt{\Delta}=\sqrt{892}=\sqrt{4*223}=\sqrt{4}*\sqrt{223}=2\sqrt{223}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{223}}{2*2}=\frac{30-2\sqrt{223}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{223}}{2*2}=\frac{30+2\sqrt{223}}{4}
$