5x^2-14x-7=7

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Solution for 5x^2-14x-7=7 equation:



5x^2-14x-7=7
We move all terms to the left:
5x^2-14x-7-(7)=0
We add all the numbers together, and all the variables
5x^2-14x-14=0
a = 5; b = -14; c = -14;
Δ = b2-4ac
Δ = -142-4·5·(-14)
Δ = 476
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:
$\sqrt{\Delta}=\sqrt{476}=\sqrt{4*119}=\sqrt{4}*\sqrt{119}=2\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{119}}{2*5}=\frac{14-2\sqrt{119}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{119}}{2*5}=\frac{14+2\sqrt{119}}{10} $

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