72(x+3)=7x2+7

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Solution for 72(x+3)=7x2+7 equation:



72(x+3)=7x^2+7
We move all terms to the left:
72(x+3)-(7x^2+7)=0
We multiply parentheses
72x-(7x^2+7)+216=0
We get rid of parentheses
-7x^2+72x-7+216=0
We add all the numbers together, and all the variables
-7x^2+72x+209=0
a = -7; b = 72; c = +209;
Δ = b2-4ac
Δ = 722-4·(-7)·209
Δ = 11036
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:
$\sqrt{\Delta}=\sqrt{11036}=\sqrt{4*2759}=\sqrt{4}*\sqrt{2759}=2\sqrt{2759}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-2\sqrt{2759}}{2*-7}=\frac{-72-2\sqrt{2759}}{-14} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+2\sqrt{2759}}{2*-7}=\frac{-72+2\sqrt{2759}}{-14} $

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