(x(5x+1)+2(5x+3))/2=3

Solution for (x(5x+1)+2(5x+3))/2=3 equation:

(x(5x+1)+2(5x+3))/2=3

We move all terms to the left:

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

We multiply all the terms by the denominator


(x(5x+1)+2(5x+3))-3*2=0


We calculate terms in parentheses: +(x(5x+1)+2(5x+3)), so:

x(5x+1)+2(5x+3)

We multiply parentheses

5x^2+x+10x+6

We add all the numbers together, and all the variables

5x^2+11x+6

Back to the equation:

+(5x^2+11x+6)


We add all the numbers together, and all the variables

(5x^2+11x+6)-6=0

We get rid of parentheses

5x^2+11x+6-6=0

We add all the numbers together, and all the variables

5x^2+11x=0

a = 5; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·5·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*5}=\frac{-22}{10}
=-2+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*5}=\frac{0}{10}
=0
$