(20+2x)(15+2x)=600

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Solution for (20+2x)(15+2x)=600 equation:



(20+2x)(15+2x)=600
We move all terms to the left:
(20+2x)(15+2x)-(600)=0
We add all the numbers together, and all the variables
(2x+20)(2x+15)-600=0
We multiply parentheses ..
(+4x^2+30x+40x+300)-600=0
We get rid of parentheses
4x^2+30x+40x+300-600=0
We add all the numbers together, and all the variables
4x^2+70x-300=0
a = 4; b = 70; c = -300;
Δ = b2-4ac
Δ = 702-4·4·(-300)
Δ = 9700
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:
$\sqrt{\Delta}=\sqrt{9700}=\sqrt{100*97}=\sqrt{100}*\sqrt{97}=10\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-10\sqrt{97}}{2*4}=\frac{-70-10\sqrt{97}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+10\sqrt{97}}{2*4}=\frac{-70+10\sqrt{97}}{8} $

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