3/5(5.2-3m)=71/10(2m+7.5)

Solution for 3/5(5.2-3m)=71/10(2m+7.5) equation:

3/5(5.2-3m)=71/10(2m+7.5)

We move all terms to the left:

3/5(5.2-3m)-(71/10(2m+7.5))=0


Domain of the equation: 5(5.2-3m)!=0

m∈R



Domain of the equation: 10(2m+7.5))!=0

m∈R


We add all the numbers together, and all the variables

3/5(-3m+5.2)-(71/10(2m+7.5))=0

We calculate fractions


(30m2/(5(-3m+5.2)*10(2m+7.5)))+(-355m0/(5(-3m+5.2)*10(2m+7.5)))=0


We calculate terms in parentheses: +(30m2/(5(-3m+5.2)*10(2m+7.5))), so:

30m2/(5(-3m+5.2)*10(2m+7.5))

We multiply all the terms by the denominator


30m2

We add all the numbers together, and all the variables

30m^2

Back to the equation:

+(30m^2)



We calculate terms in parentheses: +(-355m0/(5(-3m+5.2)*10(2m+7.5))), so:

-355m0/(5(-3m+5.2)*10(2m+7.5))

We multiply all the terms by the denominator


-355m0

We add all the numbers together, and all the variables

-355m

Back to the equation:

+(-355m)


We get rid of parentheses

30m^2-355m=0

a = 30; b = -355; c = 0;
Δ = b2-4ac
Δ = -3552-4·30·0
Δ = 126025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{126025}=355$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-355)-355}{2*30}=\frac{0}{60}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-355)+355}{2*30}=\frac{710}{60}
=11+5/6
$