3x+4=2/5x+30

Solution for 3x+4=2/5x+30 equation:

3x+4=2/5x+30

We move all terms to the left:

3x+4-(2/5x+30)=0


Domain of the equation: 5x+30)!=0

x∈R


We get rid of parentheses

3x-2/5x-30+4=0

We multiply all the terms by the denominator


3x*5x-30*5x+4*5x-2=0

Wy multiply elements

15x^2-150x+20x-2=0

We add all the numbers together, and all the variables

15x^2-130x-2=0

a = 15; b = -130; c = -2;
Δ = b2-4ac
Δ = -1302-4·15·(-2)
Δ = 17020
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:

$\sqrt{\Delta}=\sqrt{17020}=\sqrt{4*4255}=\sqrt{4}*\sqrt{4255}=2\sqrt{4255}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{4255}}{2*15}=\frac{130-2\sqrt{4255}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{4255}}{2*15}=\frac{130+2\sqrt{4255}}{30}
$