Y=2x2+7x+5

Solution for Y=2x2+7x+5 equation:

=2Y^2+7Y+5

We move all terms to the left:

-(2Y^2+7Y+5)=0

We get rid of parentheses

-2Y^2-7Y-5=0

a = -2; b = -7; c = -5;
Δ = b2-4ac
Δ = -72-4·(-2)·(-5)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3}{2*-2}=\frac{4}{-4}
=-1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3}{2*-2}=\frac{10}{-4}
=-2+1/2
$