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

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

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

We move all terms to the left:

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

We multiply parentheses

2x^2+8x-(x-3(x-3))=0


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

x-3(x-3)

We multiply parentheses

x-3x+9

We add all the numbers together, and all the variables

-2x+9

Back to the equation:

-(-2x+9)


We get rid of parentheses

2x^2+8x+2x-9=0

We add all the numbers together, and all the variables

2x^2+10x-9=0

a = 2; b = 10; c = -9;
Δ = b2-4ac
Δ = 102-4·2·(-9)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{43}}{2*2}=\frac{-10-2\sqrt{43}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{43}}{2*2}=\frac{-10+2\sqrt{43}}{4}
$