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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

3x^2-15x-(4(x+9))=0


We calculate terms in parentheses: -(4(x+9)), so:

4(x+9)

We multiply parentheses

4x+36

Back to the equation:

-(4x+36)


We get rid of parentheses

3x^2-15x-4x-36=0

We add all the numbers together, and all the variables

3x^2-19x-36=0

a = 3; b = -19; c = -36;
Δ = b2-4ac
Δ = -192-4·3·(-36)
Δ = 793
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{-(-19)-\sqrt{793}}{2*3}=\frac{19-\sqrt{793}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{793}}{2*3}=\frac{19+\sqrt{793}}{6}
$