14+x=3x(x+5)

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

14+x=3x(x+5)

We move all terms to the left:

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


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

3x(x+5)

We multiply parentheses

3x^2+15x

Back to the equation:

-(3x^2+15x)


We get rid of parentheses

-3x^2+x-15x+14=0

We add all the numbers together, and all the variables

-3x^2-14x+14=0

a = -3; b = -14; c = +14;
Δ = b2-4ac
Δ = -142-4·(-3)·14
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{91}}{2*-3}=\frac{14-2\sqrt{91}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{91}}{2*-3}=\frac{14+2\sqrt{91}}{-6}
$