5x^2-2x-11.25=0

Solution for 5x^2-2x-11.25=0 equation:

5x^2-2x-11.25=0

a = 5; b = -2; c = -11.25;
Δ = b2-4ac
Δ = -22-4·5·(-11.25)
Δ = 229
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-\sqrt{229}}{2*5}=\frac{2-\sqrt{229}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{229}}{2*5}=\frac{2+\sqrt{229}}{10}
$