14y^2=63y-35

Solution for 14y^2=63y-35 equation:

14y^2=63y-35

We move all terms to the left:

14y^2-(63y-35)=0

We get rid of parentheses

14y^2-63y+35=0

a = 14; b = -63; c = +35;
Δ = b2-4ac
Δ = -632-4·14·35
Δ = 2009
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:

$\sqrt{\Delta}=\sqrt{2009}=\sqrt{49*41}=\sqrt{49}*\sqrt{41}=7\sqrt{41}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-7\sqrt{41}}{2*14}=\frac{63-7\sqrt{41}}{28}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+7\sqrt{41}}{2*14}=\frac{63+7\sqrt{41}}{28}
$