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(3m+2)(m+1)=7-7m
We move all terms to the left:
(3m+2)(m+1)-(7-7m)=0
We add all the numbers together, and all the variables
(3m+2)(m+1)-(-7m+7)=0
We get rid of parentheses
(3m+2)(m+1)+7m-7=0
We multiply parentheses ..
(+3m^2+3m+2m+2)+7m-7=0
We get rid of parentheses
3m^2+3m+2m+7m+2-7=0
We add all the numbers together, and all the variables
3m^2+12m-5=0
a = 3; b = 12; c = -5;
Δ = b2-4ac
Δ = 122-4·3·(-5)
Δ = 204
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{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{51}}{2*3}=\frac{-12-2\sqrt{51}}{6}m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{51}}{2*3}=\frac{-12+2\sqrt{51}}{6}
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