x-40=3/4x

Solution for x-40=3/4x equation:

x-40=3/4x

We move all terms to the left:

x-40-(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)-40=0

We get rid of parentheses

x-3/4x-40=0

We multiply all the terms by the denominator


x*4x-40*4x-3=0

Wy multiply elements

4x^2-160x-3=0

a = 4; b = -160; c = -3;
Δ = b2-4ac
Δ = -1602-4·4·(-3)
Δ = 25648
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:

$\sqrt{\Delta}=\sqrt{25648}=\sqrt{16*1603}=\sqrt{16}*\sqrt{1603}=4\sqrt{1603}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-4\sqrt{1603}}{2*4}=\frac{160-4\sqrt{1603}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+4\sqrt{1603}}{2*4}=\frac{160+4\sqrt{1603}}{8}
$