x(-77/24)=-30

Solution for x(-77/24)=-30 equation:

x(-77/24)=-30

We move all terms to the left:

x(-77/24)-(-30)=0

We add all the numbers together, and all the variables

x(-77/24)+30=0

We multiply parentheses

-77x^2+30=0

a = -77; b = 0; c = +30;
Δ = b2-4ac
Δ = 02-4·(-77)·30
Δ = 9240
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:

$\sqrt{\Delta}=\sqrt{9240}=\sqrt{4*2310}=\sqrt{4}*\sqrt{2310}=2\sqrt{2310}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2310}}{2*-77}=\frac{0-2\sqrt{2310}}{-154}
=-\frac{2\sqrt{2310}}{-154}
=-\frac{\sqrt{2310}}{-77}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2310}}{2*-77}=\frac{0+2\sqrt{2310}}{-154}
=\frac{2\sqrt{2310}}{-154}
=\frac{\sqrt{2310}}{-77}
$