63x2-77x=-7

Solution for 63x2-77x=-7 equation:

63x^2-77x=-7

We move all terms to the left:

63x^2-77x-(-7)=0

We add all the numbers together, and all the variables

63x^2-77x+7=0

a = 63; b = -77; c = +7;
Δ = b2-4ac
Δ = -772-4·63·7
Δ = 4165
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4165}=\sqrt{49*85}=\sqrt{49}*\sqrt{85}=7\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-7\sqrt{85}}{2*63}=\frac{77-7\sqrt{85}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+7\sqrt{85}}{2*63}=\frac{77+7\sqrt{85}}{126}
$