x(x+2)2=49x

Solution for x(x+2)2=49x equation:

x(x+2)2=49x

We move all terms to the left:

x(x+2)2-(49x)=0

We add all the numbers together, and all the variables

-49x+x(x+2)2=0

We multiply parentheses

2x^2-49x+4x=0

We add all the numbers together, and all the variables

2x^2-45x=0

a = 2; b = -45; c = 0;
Δ = b2-4ac
Δ = -452-4·2·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-45}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+45}{2*2}=\frac{90}{4}
=22+1/2
$