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

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

X(4X+5)=2X(X-3)

We move all terms to the left:

X(4X+5)-(2X(X-3))=0

We multiply parentheses

4X^2+5X-(2X(X-3))=0


We calculate terms in parentheses: -(2X(X-3)), so:

2X(X-3)

We multiply parentheses

2X^2-6X

Back to the equation:

-(2X^2-6X)


We get rid of parentheses

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

We add all the numbers together, and all the variables

2X^2+11X=0

a = 2; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·2·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*2}=\frac{-22}{4}
=-5+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*2}=\frac{0}{4}
=0
$