-5x-10=16/3x-41

Solution for -5x-10=16/3x-41 equation:

-5x-10=16/3x-41

We move all terms to the left:

-5x-10-(16/3x-41)=0


Domain of the equation: 3x-41)!=0

x∈R


We get rid of parentheses

-5x-16/3x+41-10=0

We multiply all the terms by the denominator


-5x*3x+41*3x-10*3x-16=0

Wy multiply elements

-15x^2+123x-30x-16=0

We add all the numbers together, and all the variables

-15x^2+93x-16=0

a = -15; b = 93; c = -16;
Δ = b2-4ac
Δ = 932-4·(-15)·(-16)
Δ = 7689
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{-(93)-\sqrt{7689}}{2*-15}=\frac{-93-\sqrt{7689}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(93)+\sqrt{7689}}{2*-15}=\frac{-93+\sqrt{7689}}{-30}
$