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6x^2-38x-144=0
a = 6; b = -38; c = -144;
Δ = b2-4ac
Δ = -382-4·6·(-144)
Δ = 4900
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{4900}=70$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-70}{2*6}=\frac{-32}{12} =-2+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+70}{2*6}=\frac{108}{12} =9 $
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