2/5x+9=3x-4

Solution for 2/5x+9=3x-4 equation:

2/5x+9=3x-4

We move all terms to the left:

2/5x+9-(3x-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-3x+4+9=0

We multiply all the terms by the denominator


-3x*5x+4*5x+9*5x+2=0

Wy multiply elements

-15x^2+20x+45x+2=0

We add all the numbers together, and all the variables

-15x^2+65x+2=0

a = -15; b = 65; c = +2;
Δ = b2-4ac
Δ = 652-4·(-15)·2
Δ = 4345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-\sqrt{4345}}{2*-15}=\frac{-65-\sqrt{4345}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{4345}}{2*-15}=\frac{-65+\sqrt{4345}}{-30}
$