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10x^2-12x-74=0
a = 10; b = -12; c = -74;
Δ = b2-4ac
Δ = -122-4·10·(-74)
Δ = 3104
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3104}=\sqrt{16*194}=\sqrt{16}*\sqrt{194}=4\sqrt{194}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{194}}{2*10}=\frac{12-4\sqrt{194}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{194}}{2*10}=\frac{12+4\sqrt{194}}{20} $
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