Y=5x^2+3-10x

Solution for Y=5x^2+3-10x equation:

=5Y^2+3-10Y

We move all terms to the left:

-(5Y^2+3-10Y)=0

We get rid of parentheses

-5Y^2+10Y-3=0

a = -5; b = 10; c = -3;
Δ = b2-4ac
Δ = 102-4·(-5)·(-3)
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{10}}{2*-5}=\frac{-10-2\sqrt{10}}{-10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{10}}{2*-5}=\frac{-10+2\sqrt{10}}{-10}
$