2(3x)(x+10)=(4x+5x)(2x-4)

Solution for 2(3x)(x+10)=(4x+5x)(2x-4) equation:

2(3x)(x+10)=(4x+5x)(2x-4)

We move all terms to the left:

2(3x)(x+10)-((4x+5x)(2x-4))=0

We add all the numbers together, and all the variables

23x(x+10)-((+9x)(2x-4))=0

We multiply parentheses

23x^2+230x-((+9x)(2x-4))=0

We multiply parentheses ..

23x^2-((+18x^2-36x))+230x=0


We calculate terms in parentheses: -((+18x^2-36x)), so:

(+18x^2-36x)

We get rid of parentheses

18x^2-36x

Back to the equation:

-(18x^2-36x)


We add all the numbers together, and all the variables

23x^2+230x-(18x^2-36x)=0

We get rid of parentheses

23x^2-18x^2+230x+36x=0

We add all the numbers together, and all the variables

5x^2+266x=0

a = 5; b = 266; c = 0;
Δ = b2-4ac
Δ = 2662-4·5·0
Δ = 70756
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{70756}=266$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(266)-266}{2*5}=\frac{-532}{10}
=-53+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(266)+266}{2*5}=\frac{0}{10}
=0
$