-77x+105x^2-84=0

Solution for -77x+105x^2-84=0 equation:

-77x+105x^2-84=0

a = 105; b = -77; c = -84;
Δ = b2-4ac
Δ = -772-4·105·(-84)
Δ = 41209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{41209}=203$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-203}{2*105}=\frac{-126}{210}
=-3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+203}{2*105}=\frac{280}{210}
=1+1/3
$