14y2-77y=-35

Solution for 14y2-77y=-35 equation:

14y^2-77y=-35

We move all terms to the left:

14y^2-77y-(-35)=0

We add all the numbers together, and all the variables

14y^2-77y+35=0

a = 14; b = -77; c = +35;
Δ = b2-4ac
Δ = -772-4·14·35
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-63}{2*14}=\frac{14}{28}
=1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+63}{2*14}=\frac{140}{28}
=5
$