2m/5(1-3m)+5/8=0

Solution for 2m/5(1-3m)+5/8=0 equation:

2m/5(1-3m)+5/8=0


Domain of the equation: 5(1-3m)!=0

m∈R


We add all the numbers together, and all the variables

2m/5(-3m+1)+5/8=0

We calculate fractions


16m/(-120m+40)+(25m(-)/(-120m+40)=0


We calculate terms in parentheses: +(25m(-)/(-120m+40), so:

25m(-)/(-120m+40

We add all the numbers together, and all the variables

25m0/(-120m+40

We multiply all the terms by the denominator


25m0

We add all the numbers together, and all the variables

25m

Back to the equation:

+(25m)


We add all the numbers together, and all the variables

25m+16m/(-120m+40)=0

We multiply all the terms by the denominator


25m*(-120m+40)+16m=0

We add all the numbers together, and all the variables

16m+25m*(-120m+40)=0

We multiply parentheses

-3000m^2+16m+1000m=0

We add all the numbers together, and all the variables

-3000m^2+1016m=0

a = -3000; b = 1016; c = 0;
Δ = b2-4ac
Δ = 10162-4·(-3000)·0
Δ = 1032256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1032256}=1016$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1016)-1016}{2*-3000}=\frac{-2032}{-6000}
=127/375
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1016)+1016}{2*-3000}=\frac{0}{-6000}
=0
$