x+3=-2/5x-11

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

x+3=-2/5x-11

We move all terms to the left:

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


Domain of the equation: 5x-11)!=0

x∈R


We get rid of parentheses

x+2/5x+11+3=0

We multiply all the terms by the denominator


x*5x+11*5x+3*5x+2=0

Wy multiply elements

5x^2+55x+15x+2=0

We add all the numbers together, and all the variables

5x^2+70x+2=0

a = 5; b = 70; c = +2;
Δ = b2-4ac
Δ = 702-4·5·2
Δ = 4860
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:

$\sqrt{\Delta}=\sqrt{4860}=\sqrt{324*15}=\sqrt{324}*\sqrt{15}=18\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-18\sqrt{15}}{2*5}=\frac{-70-18\sqrt{15}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+18\sqrt{15}}{2*5}=\frac{-70+18\sqrt{15}}{10}
$