5x2-5x-14=1

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Solution for 5x2-5x-14=1 equation:



5x^2-5x-14=1
We move all terms to the left:
5x^2-5x-14-(1)=0
We add all the numbers together, and all the variables
5x^2-5x-15=0
a = 5; b = -5; c = -15;
Δ = b2-4ac
Δ = -52-4·5·(-15)
Δ = 325
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:
$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{13}}{2*5}=\frac{5-5\sqrt{13}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{13}}{2*5}=\frac{5+5\sqrt{13}}{10} $

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