X(x+23)=2x(2x+7)

Solution for X(x+23)=2x(2x+7) equation:

X(X+23)=2X(2X+7)

We move all terms to the left:

X(X+23)-(2X(2X+7))=0

We multiply parentheses

X^2+23X-(2X(2X+7))=0


We calculate terms in parentheses: -(2X(2X+7)), so:

2X(2X+7)

We multiply parentheses

4X^2+14X

Back to the equation:

-(4X^2+14X)


We get rid of parentheses

X^2-4X^2+23X-14X=0

We add all the numbers together, and all the variables

-3X^2+9X=0

a = -3; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-3)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-3}=\frac{-18}{-6}
=+3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-3}=\frac{0}{-6}
=0
$