3.7=0.05x^2+0.05x+1

Solution for 3.7=0.05x^2+0.05x+1 equation:

3.7=0.05x^2+0.05x+1

We move all terms to the left:

3.7-(0.05x^2+0.05x+1)=0

We get rid of parentheses

-0.05x^2-0.05x-1+3.7=0

We add all the numbers together, and all the variables

-0.05x^2-0.05x+2.7=0

a = -0.05; b = -0.05; c = +2.7;
Δ = b2-4ac
Δ = -0.052-4·(-0.05)·2.7
Δ = 0.5425
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.05)-\sqrt{0.5425}}{2*-0.05}=\frac{0.05-\sqrt{0.5425}}{-0.1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.05)+\sqrt{0.5425}}{2*-0.05}=\frac{0.05+\sqrt{0.5425}}{-0.1}
$