9x+4=5x(x+3)

Solution for 9x+4=5x(x+3) equation:

9x+4=5x(x+3)

We move all terms to the left:

9x+4-(5x(x+3))=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+9x-15x+4=0

We add all the numbers together, and all the variables

-5x^2-6x+4=0

a = -5; b = -6; c = +4;
Δ = b2-4ac
Δ = -62-4·(-5)·4
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{29}}{2*-5}=\frac{6-2\sqrt{29}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{29}}{2*-5}=\frac{6+2\sqrt{29}}{-10}
$