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

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

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

We move all terms to the left:

2m+5-(5(m-7)3m)=0


We calculate terms in parentheses: -(5(m-7)3m), so:

5(m-7)3m

We multiply parentheses

15m^2-105m

Back to the equation:

-(15m^2-105m)


We get rid of parentheses

-15m^2+2m+105m+5=0

We add all the numbers together, and all the variables

-15m^2+107m+5=0

a = -15; b = 107; c = +5;
Δ = b2-4ac
Δ = 1072-4·(-15)·5
Δ = 11749
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{-(107)-\sqrt{11749}}{2*-15}=\frac{-107-\sqrt{11749}}{-30}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(107)+\sqrt{11749}}{2*-15}=\frac{-107+\sqrt{11749}}{-30}
$