3x(x+4)=5(x-6)+32

Solution for 3x(x+4)=5(x-6)+32 equation:

3x(x+4)=5(x-6)+32

We move all terms to the left:

3x(x+4)-(5(x-6)+32)=0

We multiply parentheses

3x^2+12x-(5(x-6)+32)=0


We calculate terms in parentheses: -(5(x-6)+32), so:

5(x-6)+32

We multiply parentheses

5x-30+32

We add all the numbers together, and all the variables

5x+2

Back to the equation:

-(5x+2)


We get rid of parentheses

3x^2+12x-5x-2=0

We add all the numbers together, and all the variables

3x^2+7x-2=0

a = 3; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·3·(-2)
Δ = 73
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{-(7)-\sqrt{73}}{2*3}=\frac{-7-\sqrt{73}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{73}}{2*3}=\frac{-7+\sqrt{73}}{6}
$