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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

5x^2-3x+10x-(x+11)=0

We get rid of parentheses

5x^2-3x+10x-x-11=0

We add all the numbers together, and all the variables

5x^2+6x-11=0

a = 5; b = 6; c = -11;
Δ = b2-4ac
Δ = 62-4·5·(-11)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-16}{2*5}=\frac{-22}{10}
=-2+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+16}{2*5}=\frac{10}{10}
=1
$