Y=3x^2+7x+1

Solution for Y=3x^2+7x+1 equation:

=3Y^2+7Y+1

We move all terms to the left:

-(3Y^2+7Y+1)=0

We get rid of parentheses

-3Y^2-7Y-1=0

a = -3; b = -7; c = -1;
Δ = b2-4ac
Δ = -72-4·(-3)·(-1)
Δ = 37
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{-(-7)-\sqrt{37}}{2*-3}=\frac{7-\sqrt{37}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{37}}{2*-3}=\frac{7+\sqrt{37}}{-6}
$