7.5x^2+20x+12=0

Solution for 7.5x^2+20x+12=0 equation:

7.5x^2+20x+12=0

a = 7.5; b = 20; c = +12;
Δ = b2-4ac
Δ = 202-4·7.5·12
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{10}}{2*7.5}=\frac{-20-2\sqrt{10}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{10}}{2*7.5}=\frac{-20+2\sqrt{10}}{15}
$