Y=x^2-10.3x+10

Solution for Y=x^2-10.3x+10 equation:

=Y^2-10.3Y+10

We move all terms to the left:

-(Y^2-10.3Y+10)=0

We get rid of parentheses

-Y^2+10.3Y-10=0

We add all the numbers together, and all the variables

-1Y^2+10.3Y-10=0

a = -1; b = 10.3; c = -10;
Δ = b2-4ac
Δ = 10.32-4·(-1)·(-10)
Δ = 66.09
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10.3)-\sqrt{66.09}}{2*-1}=\frac{-10.3-\sqrt{66.09}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10.3)+\sqrt{66.09}}{2*-1}=\frac{-10.3+\sqrt{66.09}}{-2}
$