1=-0.009(m-6.66)(m-6.66)+1.40

Solution for 1=-0.009(m-6.66)(m-6.66)+1.40 equation:

1=-0.009(m-6.66)(m-6.66)+1.40

We move all terms to the left:

1-(-0.009(m-6.66)(m-6.66)+1.40)=0

We multiply parentheses ..

-(-0.009(+m^2-6.66m-6.66m+44.3556)+1.40)+1=0


We calculate terms in parentheses: -(-0.009(+m^2-6.66m-6.66m+44.3556)+1.40), so:

-0.009(+m^2-6.66m-6.66m+44.3556)+1.40

We add all the numbers together, and all the variables

-0.009(+m^2-6.66m-6.66m+44.3556)+1.4

We multiply parentheses

-0.009m^2+0.054m+0.054m-0.3992004+1.4

We add all the numbers together, and all the variables

-0.009m^2+0.108m+1.0007996

Back to the equation:

-(-0.009m^2+0.108m+1.0007996)


We get rid of parentheses

0.009m^2-0.108m-1.0007996+1=0

We add all the numbers together, and all the variables

0.009m^2-0.108m-0.0007995999999999=0

a = 0.009; b = -0.108; c = -0.0007995999999999;
Δ = b2-4ac
Δ = -0.1082-4·0.009·(-0.0007995999999999)
Δ = 0.0116927856
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{-(-0.108)-\sqrt{0.0116927856}}{2*0.009}=\frac{0.108-\sqrt{0.0116927856}}{0.018}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.108)+\sqrt{0.0116927856}}{2*0.009}=\frac{0.108+\sqrt{0.0116927856}}{0.018}
$