X=1/4x+7

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

X=1/4X+7

We move all terms to the left:

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


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

X∈R


We get rid of parentheses

X-1/4X-7=0

We multiply all the terms by the denominator


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

Wy multiply elements

4X^2-28X-1=0

a = 4; b = -28; c = -1;
Δ = b2-4ac
Δ = -282-4·4·(-1)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-20\sqrt{2}}{2*4}=\frac{28-20\sqrt{2}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+20\sqrt{2}}{2*4}=\frac{28+20\sqrt{2}}{8}
$