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4x(10+4x)=440
We move all terms to the left:
4x(10+4x)-(440)=0
We add all the numbers together, and all the variables
4x(4x+10)-440=0
We multiply parentheses
16x^2+40x-440=0
a = 16; b = 40; c = -440;
Δ = b2-4ac
Δ = 402-4·16·(-440)
Δ = 29760
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{29760}=\sqrt{64*465}=\sqrt{64}*\sqrt{465}=8\sqrt{465}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{465}}{2*16}=\frac{-40-8\sqrt{465}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{465}}{2*16}=\frac{-40+8\sqrt{465}}{32} $
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