12x(x+4)+2=5(5x+2)+1

Solution for 12x(x+4)+2=5(5x+2)+1 equation:

12x(x+4)+2=5(5x+2)+1

We move all terms to the left:

12x(x+4)+2-(5(5x+2)+1)=0

We multiply parentheses

12x^2+48x-(5(5x+2)+1)+2=0


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

5(5x+2)+1

We multiply parentheses

25x+10+1

We add all the numbers together, and all the variables

25x+11

Back to the equation:

-(25x+11)


We get rid of parentheses

12x^2+48x-25x-11+2=0

We add all the numbers together, and all the variables

12x^2+23x-9=0

a = 12; b = 23; c = -9;
Δ = b2-4ac
Δ = 232-4·12·(-9)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-31}{2*12}=\frac{-54}{24}
=-2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+31}{2*12}=\frac{8}{24}
=1/3
$