1x+9=5x(x+3)

Solution for 1x+9=5x(x+3) equation:

1x+9=5x(x+3)

We move all terms to the left:

1x+9-(5x(x+3))=0

We add all the numbers together, and all the variables

x-(5x(x+3))+9=0


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

5x(x+3)

We multiply parentheses

5x^2+15x

Back to the equation:

-(5x^2+15x)


We get rid of parentheses

-5x^2+x-15x+9=0

We add all the numbers together, and all the variables

-5x^2-14x+9=0

a = -5; b = -14; c = +9;
Δ = b2-4ac
Δ = -142-4·(-5)·9
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{94}}{2*-5}=\frac{14-2\sqrt{94}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{94}}{2*-5}=\frac{14+2\sqrt{94}}{-10}
$