25x(x*2+3x)=2(2x+6)

Solution for 25x(x*2+3x)=2(2x+6) equation:

25x(x*2+3x)=2(2x+6)

We move all terms to the left:

25x(x*2+3x)-(2(2x+6))=0

We add all the numbers together, and all the variables

25x(+3x+x*2)-(2(2x+6))=0

We multiply parentheses

75x^2+50x^2-(2(2x+6))=0


We calculate terms in parentheses: -(2(2x+6)), so:

2(2x+6)

We multiply parentheses

4x+12

Back to the equation:

-(4x+12)


We add all the numbers together, and all the variables

125x^2-(4x+12)=0

We get rid of parentheses

125x^2-4x-12=0

a = 125; b = -4; c = -12;
Δ = b2-4ac
Δ = -42-4·125·(-12)
Δ = 6016
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:

$\sqrt{\Delta}=\sqrt{6016}=\sqrt{64*94}=\sqrt{64}*\sqrt{94}=8\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{94}}{2*125}=\frac{4-8\sqrt{94}}{250}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{94}}{2*125}=\frac{4+8\sqrt{94}}{250}
$