10=0.2x2-1.02x

Solution for 10=0.2x2-1.02x equation:

10=0.2x^2-1.02x

We move all terms to the left:

10-(0.2x^2-1.02x)=0

We get rid of parentheses

-0.2x^2+1.02x+10=0

a = -0.2; b = 1.02; c = +10;
Δ = b2-4ac
Δ = 1.022-4·(-0.2)·10
Δ = 9.0404
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{-(1.02)-\sqrt{9.0404}}{2*-0.2}=\frac{-1.02-\sqrt{9.0404}}{-0.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.02)+\sqrt{9.0404}}{2*-0.2}=\frac{-1.02+\sqrt{9.0404}}{-0.4}
$