y=7x2+2x-3

Solution for y=7x2+2x-3 equation:

=7Y^2+2Y-3

We move all terms to the left:

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

We get rid of parentheses

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

a = -7; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-7)·3
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{22}}{2*-7}=\frac{2-2\sqrt{22}}{-14}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{22}}{2*-7}=\frac{2+2\sqrt{22}}{-14}
$