3x(4-2)+5x=2(x+9)

Solution for 3x(4-2)+5x=2(x+9) equation:

3x(4-2)+5x=2(x+9)

We move all terms to the left:

3x(4-2)+5x-(2(x+9))=0

We add all the numbers together, and all the variables

3x2+5x-(2(x+9))=0

We add all the numbers together, and all the variables

3x^2+5x-(2(x+9))=0


We calculate terms in parentheses: -(2(x+9)), so:

2(x+9)

We multiply parentheses

2x+18

Back to the equation:

-(2x+18)


We get rid of parentheses

3x^2+5x-2x-18=0

We add all the numbers together, and all the variables

3x^2+3x-18=0

a = 3; b = 3; c = -18;
Δ = b2-4ac
Δ = 32-4·3·(-18)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-15}{2*3}=\frac{-18}{6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+15}{2*3}=\frac{12}{6}
=2
$