Y=10x^2+38x+30

Solution for Y=10x^2+38x+30 equation:

=10Y^2+38Y+30

We move all terms to the left:

-(10Y^2+38Y+30)=0

We get rid of parentheses

-10Y^2-38Y-30=0

a = -10; b = -38; c = -30;
Δ = b2-4ac
Δ = -382-4·(-10)·(-30)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{61}}{2*-10}=\frac{38-2\sqrt{61}}{-20}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{61}}{2*-10}=\frac{38+2\sqrt{61}}{-20}
$