10/3x+4=5x-1

Solution for 10/3x+4=5x-1 equation:

10/3x+4=5x-1

We move all terms to the left:

10/3x+4-(5x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

10/3x-5x+1+4=0

We multiply all the terms by the denominator


-5x*3x+1*3x+4*3x+10=0

Wy multiply elements

-15x^2+3x+12x+10=0

We add all the numbers together, and all the variables

-15x^2+15x+10=0

a = -15; b = 15; c = +10;
Δ = b2-4ac
Δ = 152-4·(-15)·10
Δ = 825
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:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{33}}{2*-15}=\frac{-15-5\sqrt{33}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{33}}{2*-15}=\frac{-15+5\sqrt{33}}{-30}
$