X(2x+5)=(x+7)

Solution for X(2x+5)=(x+7) equation:

X(2X+5)=(X+7)

We move all terms to the left:

X(2X+5)-((X+7))=0

We multiply parentheses

2X^2+5X-((X+7))=0


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

(X+7)

We get rid of parentheses

X+7

Back to the equation:

-(X+7)


We get rid of parentheses

2X^2+5X-X-7=0

We add all the numbers together, and all the variables

2X^2+4X-7=0

a = 2; b = 4; c = -7;
Δ = b2-4ac
Δ = 42-4·2·(-7)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6\sqrt{2}}{2*2}=\frac{-4-6\sqrt{2}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6\sqrt{2}}{2*2}=\frac{-4+6\sqrt{2}}{4}
$