13x^2+12x-77=0

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Solution for 13x^2+12x-77=0 equation:



13x^2+12x-77=0
a = 13; b = 12; c = -77;
Δ = b2-4ac
Δ = 122-4·13·(-77)
Δ = 4148
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:
$\sqrt{\Delta}=\sqrt{4148}=\sqrt{4*1037}=\sqrt{4}*\sqrt{1037}=2\sqrt{1037}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{1037}}{2*13}=\frac{-12-2\sqrt{1037}}{26} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{1037}}{2*13}=\frac{-12+2\sqrt{1037}}{26} $

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