X-2=-1/4x+7

Solution for X-2=-1/4x+7 equation:

X-2=-1/4X+7

We move all terms to the left:

X-2-(-1/4X+7)=0


Domain of the equation: 4X+7)!=0

X∈R


We get rid of parentheses

X+1/4X-7-2=0

We multiply all the terms by the denominator


X*4X-7*4X-2*4X+1=0

Wy multiply elements

4X^2-28X-8X+1=0

We add all the numbers together, and all the variables

4X^2-36X+1=0

a = 4; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·4·1
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-16\sqrt{5}}{2*4}=\frac{36-16\sqrt{5}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+16\sqrt{5}}{2*4}=\frac{36+16\sqrt{5}}{8}
$