4,5x^2+3x=72

Solution for 4,5x^2+3x=72 equation:

4.5x^2+3x=72

We move all terms to the left:

4.5x^2+3x-(72)=0

a = 4.5; b = 3; c = -72;
Δ = b2-4ac
Δ = 32-4·4.5·(-72)
Δ = 1305
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:

$\sqrt{\Delta}=\sqrt{1305}=\sqrt{9*145}=\sqrt{9}*\sqrt{145}=3\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{145}}{2*4.5}=\frac{-3-3\sqrt{145}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{145}}{2*4.5}=\frac{-3+3\sqrt{145}}{9}
$