11-(1/6)(18h+12)=-4h-10

Solution for 11-(1/6)(18h+12)=-4h-10 equation:

11-(1/6)(18h+12)=-4h-10

We move all terms to the left:

11-(1/6)(18h+12)-(-4h-10)=0


Domain of the equation: 6)(18h+12)!=0

h∈R


We add all the numbers together, and all the variables

-(+1/6)(18h+12)-(-4h-10)+11=0

We get rid of parentheses

-(+1/6)(18h+12)+4h+10+11=0

We multiply parentheses ..

-(+18h^2+1/6*12)+4h+10+11=0

We multiply all the terms by the denominator


-(+18h^2+1+4h*6*12)+10*6*12)+11*6*12)=0

We add all the numbers together, and all the variables

-(+18h^2+1+4h*6*12)=0

We get rid of parentheses

-18h^2-4h*6*12-1=0

Wy multiply elements

-18h^2-288h*1-1=0

Wy multiply elements

-18h^2-288h-1=0

a = -18; b = -288; c = -1;
Δ = b2-4ac
Δ = -2882-4·(-18)·(-1)
Δ = 82872
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{82872}=\sqrt{36*2302}=\sqrt{36}*\sqrt{2302}=6\sqrt{2302}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-6\sqrt{2302}}{2*-18}=\frac{288-6\sqrt{2302}}{-36}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+6\sqrt{2302}}{2*-18}=\frac{288+6\sqrt{2302}}{-36}
$