14x+4=12x(x+2)

Solution for 14x+4=12x(x+2) equation:

14x+4=12x(x+2)

We move all terms to the left:

14x+4-(12x(x+2))=0


We calculate terms in parentheses: -(12x(x+2)), so:

12x(x+2)

We multiply parentheses

12x^2+24x

Back to the equation:

-(12x^2+24x)


We get rid of parentheses

-12x^2+14x-24x+4=0

We add all the numbers together, and all the variables

-12x^2-10x+4=0

a = -12; b = -10; c = +4;
Δ = b2-4ac
Δ = -102-4·(-12)·4
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{73}}{2*-12}=\frac{10-2\sqrt{73}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{73}}{2*-12}=\frac{10+2\sqrt{73}}{-24}
$