3x(x+3)=7.5

Solution for 3x(x+3)=7.5 equation:

3x(x+3)=7.5

We move all terms to the left:

3x(x+3)-(7.5)=0

We add all the numbers together, and all the variables

3x(x+3)-7.5=0

We multiply parentheses

3x^2+9x-7.5=0

a = 3; b = 9; c = -7.5;
Δ = b2-4ac
Δ = 92-4·3·(-7.5)
Δ = 171
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:

$\sqrt{\Delta}=\sqrt{171}=\sqrt{9*19}=\sqrt{9}*\sqrt{19}=3\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{19}}{2*3}=\frac{-9-3\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{19}}{2*3}=\frac{-9+3\sqrt{19}}{6}
$