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6x^2+36x+23=0
a = 6; b = 36; c = +23;
Δ = b2-4ac
Δ = 362-4·6·23
Δ = 744
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{186}}{2*6}=\frac{-36-2\sqrt{186}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{186}}{2*6}=\frac{-36+2\sqrt{186}}{12} $
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