54x^2-15x-2500=0

Solution for 54x^2-15x-2500=0 equation:

54x^2-15x-2500=0

a = 54; b = -15; c = -2500;
Δ = b2-4ac
Δ = -152-4·54·(-2500)
Δ = 540225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{540225}=735$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-735}{2*54}=\frac{-720}{108}
=-6+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+735}{2*54}=\frac{750}{108}
=6+17/18
$