5x+2=3x(x+14)

Solution for 5x+2=3x(x+14) equation:

5x+2=3x(x+14)

We move all terms to the left:

5x+2-(3x(x+14))=0


We calculate terms in parentheses: -(3x(x+14)), so:

3x(x+14)

We multiply parentheses

3x^2+42x

Back to the equation:

-(3x^2+42x)


We get rid of parentheses

-3x^2+5x-42x+2=0

We add all the numbers together, and all the variables

-3x^2-37x+2=0

a = -3; b = -37; c = +2;
Δ = b2-4ac
Δ = -372-4·(-3)·2
Δ = 1393
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-\sqrt{1393}}{2*-3}=\frac{37-\sqrt{1393}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{1393}}{2*-3}=\frac{37+\sqrt{1393}}{-6}
$