11-(1/3)(12m+15)=-5m-13

Solution for 11-(1/3)(12m+15)=-5m-13 equation:

11-(1/3)(12m+15)=-5m-13

We move all terms to the left:

11-(1/3)(12m+15)-(-5m-13)=0


Domain of the equation: 3)(12m+15)!=0

m∈R


We add all the numbers together, and all the variables

-(+1/3)(12m+15)-(-5m-13)+11=0

We get rid of parentheses

-(+1/3)(12m+15)+5m+13+11=0

We multiply parentheses ..

-(+12m^2+1/3*15)+5m+13+11=0

We multiply all the terms by the denominator


-(+12m^2+1+5m*3*15)+13*3*15)+11*3*15)=0

We add all the numbers together, and all the variables

-(+12m^2+1+5m*3*15)=0

We get rid of parentheses

-12m^2-5m*3*15-1=0

Wy multiply elements

-12m^2-225m*1-1=0

Wy multiply elements

-12m^2-225m-1=0

a = -12; b = -225; c = -1;
Δ = b2-4ac
Δ = -2252-4·(-12)·(-1)
Δ = 50577
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{-(-225)-\sqrt{50577}}{2*-12}=\frac{225-\sqrt{50577}}{-24}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-225)+\sqrt{50577}}{2*-12}=\frac{225+\sqrt{50577}}{-24}
$