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4x^2-68x+111=0
a = 4; b = -68; c = +111;
Δ = b2-4ac
Δ = -682-4·4·111
Δ = 2848
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2848}=\sqrt{16*178}=\sqrt{16}*\sqrt{178}=4\sqrt{178}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{178}}{2*4}=\frac{68-4\sqrt{178}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{178}}{2*4}=\frac{68+4\sqrt{178}}{8} $
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