414=2(5x*3x+3x*1x+5x*1x)

Solution for 414=2(5x*3x+3x*1x+5x*1x) equation:

414=2(5x*3x+3x*1x+5x*1x)

We move all terms to the left:

414-(2(5x*3x+3x*1x+5x*1x))=0

We add all the numbers together, and all the variables

-(2(+5x*3x+3x*1x+5x*1x))+414=0


We calculate terms in parentheses: -(2(+5x*3x+3x*1x+5x*1x)), so:

2(+5x*3x+3x*1x+5x*1x)

We multiply parentheses

30x^2+6x^2+10x^2

We add all the numbers together, and all the variables

46x^2

Back to the equation:

-(46x^2)


a = -46; b = 0; c = +414;
Δ = b2-4ac
Δ = 02-4·(-46)·414
Δ = 76176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{76176}=276$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-276}{2*-46}=\frac{-276}{-92}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+276}{2*-46}=\frac{276}{-92}
=-3
$