1.05u=0.6u^2-0.6+1

Solution for 1.05u=0.6u^2-0.6+1 equation:

1.05u=0.6u^2-0.6+1

We move all terms to the left:

1.05u-(0.6u^2-0.6+1)=0

We get rid of parentheses

-0.6u^2+1.05u+0.6-1=0

We add all the numbers together, and all the variables

-0.6u^2+1.05u-0.4=0

a = -0.6; b = 1.05; c = -0.4;
Δ = b2-4ac
Δ = 1.052-4·(-0.6)·(-0.4)
Δ = 0.1425
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1.05)-\sqrt{0.1425}}{2*-0.6}=\frac{-1.05-\sqrt{0.1425}}{-1.2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.05)+\sqrt{0.1425}}{2*-0.6}=\frac{-1.05+\sqrt{0.1425}}{-1.2}
$