Y=4x2+7x-19

Solution for Y=4x2+7x-19 equation:

=4Y^2+7Y-19

We move all terms to the left:

-(4Y^2+7Y-19)=0

We get rid of parentheses

-4Y^2-7Y+19=0

a = -4; b = -7; c = +19;
Δ = b2-4ac
Δ = -72-4·(-4)·19
Δ = 353
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{353}}{2*-4}=\frac{7-\sqrt{353}}{-8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{353}}{2*-4}=\frac{7+\sqrt{353}}{-8}
$