5x-11/3x+7=-2/1

Solution for 5x-11/3x+7=-2/1 equation:

5x-11/3x+7=-2/1

We move all terms to the left:

5x-11/3x+7-(-2/1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5x-11/3x+7-(-2)=0

We add all the numbers together, and all the variables

5x-11/3x+9=0

We multiply all the terms by the denominator


5x*3x+9*3x-11=0

Wy multiply elements

15x^2+27x-11=0

a = 15; b = 27; c = -11;
Δ = b2-4ac
Δ = 272-4·15·(-11)
Δ = 1389
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{-(27)-\sqrt{1389}}{2*15}=\frac{-27-\sqrt{1389}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{1389}}{2*15}=\frac{-27+\sqrt{1389}}{30}
$