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6m+5m(m-1)=7
We move all terms to the left:
6m+5m(m-1)-(7)=0
We multiply parentheses
5m^2+6m-5m-7=0
We add all the numbers together, and all the variables
5m^2+m-7=0
a = 5; b = 1; c = -7;
Δ = b2-4ac
Δ = 12-4·5·(-7)
Δ = 141
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}$$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{141}}{2*5}=\frac{-1-\sqrt{141}}{10} $$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{141}}{2*5}=\frac{-1+\sqrt{141}}{10} $
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