216x+x2-81=0

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Solution for 216x+x2-81=0 equation:



216x+x2-81=0
We add all the numbers together, and all the variables
x^2+216x-81=0
a = 1; b = 216; c = -81;
Δ = b2-4ac
Δ = 2162-4·1·(-81)
Δ = 46980
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:
$\sqrt{\Delta}=\sqrt{46980}=\sqrt{324*145}=\sqrt{324}*\sqrt{145}=18\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-18\sqrt{145}}{2*1}=\frac{-216-18\sqrt{145}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+18\sqrt{145}}{2*1}=\frac{-216+18\sqrt{145}}{2} $

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