Y-7x2-14x=3

Solution for Y-7x2-14x=3 equation:

-7Y^2-14Y=3

We move all terms to the left:

-7Y^2-14Y-(3)=0

a = -7; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·(-7)·(-3)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{7}}{2*-7}=\frac{14-4\sqrt{7}}{-14}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{7}}{2*-7}=\frac{14+4\sqrt{7}}{-14}
$