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4x^2-30x-117=0
a = 4; b = -30; c = -117;
Δ = b2-4ac
Δ = -302-4·4·(-117)
Δ = 2772
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2772}=\sqrt{36*77}=\sqrt{36}*\sqrt{77}=6\sqrt{77}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{77}}{2*4}=\frac{30-6\sqrt{77}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{77}}{2*4}=\frac{30+6\sqrt{77}}{8} $
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