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(48+2x)(32+2x)=1536+336
We move all terms to the left:
(48+2x)(32+2x)-(1536+336)=0
We add all the numbers together, and all the variables
(2x+48)(2x+32)-1872=0
We multiply parentheses ..
(+4x^2+64x+96x+1536)-1872=0
We get rid of parentheses
4x^2+64x+96x+1536-1872=0
We add all the numbers together, and all the variables
4x^2+160x-336=0
a = 4; b = 160; c = -336;
Δ = b2-4ac
Δ = 1602-4·4·(-336)
Δ = 30976
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{30976}=176$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-176}{2*4}=\frac{-336}{8} =-42 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+176}{2*4}=\frac{16}{8} =2 $
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