x-4=3/5x+2

Solution for x-4=3/5x+2 equation:

x-4=3/5x+2

We move all terms to the left:

x-4-(3/5x+2)=0


Domain of the equation: 5x+2)!=0

x∈R


We get rid of parentheses

x-3/5x-2-4=0

We multiply all the terms by the denominator


x*5x-2*5x-4*5x-3=0

Wy multiply elements

5x^2-10x-20x-3=0

We add all the numbers together, and all the variables

5x^2-30x-3=0

a = 5; b = -30; c = -3;
Δ = b2-4ac
Δ = -302-4·5·(-3)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-8\sqrt{15}}{2*5}=\frac{30-8\sqrt{15}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+8\sqrt{15}}{2*5}=\frac{30+8\sqrt{15}}{10}
$