(96x+32)x=20

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Solution for (96x+32)x=20 equation:



(96x+32)x=20
We move all terms to the left:
(96x+32)x-(20)=0
We multiply parentheses
96x^2+32x-20=0
a = 96; b = 32; c = -20;
Δ = b2-4ac
Δ = 322-4·96·(-20)
Δ = 8704
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:
$\sqrt{\Delta}=\sqrt{8704}=\sqrt{256*34}=\sqrt{256}*\sqrt{34}=16\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-16\sqrt{34}}{2*96}=\frac{-32-16\sqrt{34}}{192} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+16\sqrt{34}}{2*96}=\frac{-32+16\sqrt{34}}{192} $

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