15x^2-6x-3.75=0

Solution for 15x^2-6x-3.75=0 equation:

15x^2-6x-3.75=0

a = 15; b = -6; c = -3.75;
Δ = b2-4ac
Δ = -62-4·15·(-3.75)
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-3\sqrt{29}}{2*15}=\frac{6-3\sqrt{29}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+3\sqrt{29}}{2*15}=\frac{6+3\sqrt{29}}{30}
$