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13(x2-5x-14)=1
We move all terms to the left:
13(x2-5x-14)-(1)=0
We add all the numbers together, and all the variables
13(+x^2-5x-14)-1=0
We multiply parentheses
13x^2-65x-182-1=0
We add all the numbers together, and all the variables
13x^2-65x-183=0
a = 13; b = -65; c = -183;
Δ = b2-4ac
Δ = -652-4·13·(-183)
Δ = 13741
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-\sqrt{13741}}{2*13}=\frac{65-\sqrt{13741}}{26} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{13741}}{2*13}=\frac{65+\sqrt{13741}}{26} $
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