5/3x+10=4x+3

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

5/3x+10=4x+3

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-12x^2-9x+30x+5=0

We add all the numbers together, and all the variables

-12x^2+21x+5=0

a = -12; b = 21; c = +5;
Δ = b2-4ac
Δ = 212-4·(-12)·5
Δ = 681
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{-(21)-\sqrt{681}}{2*-12}=\frac{-21-\sqrt{681}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{681}}{2*-12}=\frac{-21+\sqrt{681}}{-24}
$