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x^2-20x-64=6
We move all terms to the left:
x^2-20x-64-(6)=0
We add all the numbers together, and all the variables
x^2-20x-70=0
a = 1; b = -20; c = -70;
Δ = b2-4ac
Δ = -202-4·1·(-70)
Δ = 680
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{680}=\sqrt{4*170}=\sqrt{4}*\sqrt{170}=2\sqrt{170}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{170}}{2*1}=\frac{20-2\sqrt{170}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{170}}{2*1}=\frac{20+2\sqrt{170}}{2} $
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