X-7=3/4x

Solution for X-7=3/4x equation:

X-7=3/4X

We move all terms to the left:

X-7-(3/4X)=0


Domain of the equation: 4X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+3/4X)-7=0

We get rid of parentheses

X-3/4X-7=0

We multiply all the terms by the denominator


X*4X-7*4X-3=0

Wy multiply elements

4X^2-28X-3=0

a = 4; b = -28; c = -3;
Δ = b2-4ac
Δ = -282-4·4·(-3)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-8\sqrt{13}}{2*4}=\frac{28-8\sqrt{13}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+8\sqrt{13}}{2*4}=\frac{28+8\sqrt{13}}{8}
$