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(-3/7)(m+5)=3+2m

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Solution for (-3/7)(m+5)=3+2m equation:



(-3/7)(m+5)=3+2m
We move all terms to the left:
(-3/7)(m+5)-(3+2m)=0
Domain of the equation: 7)(m+5)!=0
m∈R
We add all the numbers together, and all the variables
(-3/7)(m+5)-(2m+3)=0
We get rid of parentheses
(-3/7)(m+5)-2m-3=0
We multiply parentheses ..
(-3m^2-3/7*5)-2m-3=0
We multiply all the terms by the denominator
(-3m^2-3-2m*7*5)-3*7*5)=0
We add all the numbers together, and all the variables
(-3m^2-3-2m*7*5)=0
We get rid of parentheses
-3m^2-2m*7*5-3=0
Wy multiply elements
-3m^2-70m*5-3=0
Wy multiply elements
-3m^2-350m-3=0
a = -3; b = -350; c = -3;
Δ = b2-4ac
Δ = -3502-4·(-3)·(-3)
Δ = 122464
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{122464}=\sqrt{16*7654}=\sqrt{16}*\sqrt{7654}=4\sqrt{7654}
m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-4\sqrt{7654}}{2*-3}=\frac{350-4\sqrt{7654}}{-6}
m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+4\sqrt{7654}}{2*-3}=\frac{350+4\sqrt{7654}}{-6}

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