7n^2=11n+4

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Solution for 7n^2=11n+4 equation:



7n^2=11n+4
We move all terms to the left:
7n^2-(11n+4)=0
We get rid of parentheses
7n^2-11n-4=0
a = 7; b = -11; c = -4;
Δ = b2-4ac
Δ = -112-4·7·(-4)
Δ = 233
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{233}}{2*7}=\frac{11-\sqrt{233}}{14} $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{233}}{2*7}=\frac{11+\sqrt{233}}{14} $

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