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4x^2-8x-65=6
We move all terms to the left:
4x^2-8x-65-(6)=0
We add all the numbers together, and all the variables
4x^2-8x-71=0
a = 4; b = -8; c = -71;
Δ = b2-4ac
Δ = -82-4·4·(-71)
Δ = 1200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-20\sqrt{3}}{2*4}=\frac{8-20\sqrt{3}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+20\sqrt{3}}{2*4}=\frac{8+20\sqrt{3}}{8} $
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