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7m^2-12m=5=0
We move all terms to the left:
7m^2-12m-(5)=0
a = 7; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·7·(-5)
Δ = 284
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{71}}{2*7}=\frac{12-2\sqrt{71}}{14} $$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{71}}{2*7}=\frac{12+2\sqrt{71}}{14} $
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