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4x^2-52x+106=0
a = 4; b = -52; c = +106;
Δ = b2-4ac
Δ = -522-4·4·106
Δ = 1008
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-12\sqrt{7}}{2*4}=\frac{52-12\sqrt{7}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+12\sqrt{7}}{2*4}=\frac{52+12\sqrt{7}}{8} $
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