3-5(2m-10)=2/3m+10

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

3-5(2m-10)=2/3m+10

We move all terms to the left:

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


Domain of the equation: 3m+10)!=0

m∈R


We multiply parentheses

-10m-(2/3m+10)+50+3=0

We get rid of parentheses

-10m-2/3m-10+50+3=0

We multiply all the terms by the denominator


-10m*3m-10*3m+50*3m+3*3m-2=0

Wy multiply elements

-30m^2-30m+150m+9m-2=0

We add all the numbers together, and all the variables

-30m^2+129m-2=0

a = -30; b = 129; c = -2;
Δ = b2-4ac
Δ = 1292-4·(-30)·(-2)
Δ = 16401
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{-(129)-\sqrt{16401}}{2*-30}=\frac{-129-\sqrt{16401}}{-60}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(129)+\sqrt{16401}}{2*-30}=\frac{-129+\sqrt{16401}}{-60}
$