3x^2-0.5x-7.5=0

Solution for 3x^2-0.5x-7.5=0 equation:

3x^2-0.5x-7.5=0

a = 3; b = -0.5; c = -7.5;
Δ = b2-4ac
Δ = -0.52-4·3·(-7.5)
Δ = 90.25
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{-(-0.5)-\sqrt{90.25}}{2*3}=\frac{0.5-\sqrt{90.25}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{90.25}}{2*3}=\frac{0.5+\sqrt{90.25}}{6}
$