414=(15+x+x)(20+x+x)

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Solution for 414=(15+x+x)(20+x+x) equation:



414=(15+x+x)(20+x+x)
We move all terms to the left:
414-((15+x+x)(20+x+x))=0
We add all the numbers together, and all the variables
-((2x+15)(2x+20))+414=0
We multiply parentheses ..
-((+4x^2+40x+30x+300))+414=0
We calculate terms in parentheses: -((+4x^2+40x+30x+300)), so:
(+4x^2+40x+30x+300)
We get rid of parentheses
4x^2+40x+30x+300
We add all the numbers together, and all the variables
4x^2+70x+300
Back to the equation:
-(4x^2+70x+300)
We get rid of parentheses
-4x^2-70x-300+414=0
We add all the numbers together, and all the variables
-4x^2-70x+114=0
a = -4; b = -70; c = +114;
Δ = b2-4ac
Δ = -702-4·(-4)·114
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-82}{2*-4}=\frac{-12}{-8} =1+1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+82}{2*-4}=\frac{152}{-8} =-19 $

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