16x(4x-5)=220

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Solution for 16x(4x-5)=220 equation:



16x(4x-5)=220
We move all terms to the left:
16x(4x-5)-(220)=0
We multiply parentheses
64x^2-80x-220=0
a = 64; b = -80; c = -220;
Δ = b2-4ac
Δ = -802-4·64·(-220)
Δ = 62720
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:
$\sqrt{\Delta}=\sqrt{62720}=\sqrt{12544*5}=\sqrt{12544}*\sqrt{5}=112\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-112\sqrt{5}}{2*64}=\frac{80-112\sqrt{5}}{128} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+112\sqrt{5}}{2*64}=\frac{80+112\sqrt{5}}{128} $

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