4.5x^2+4x=138

Solution for 4.5x^2+4x=138 equation:

4.5x^2+4x=138

We move all terms to the left:

4.5x^2+4x-(138)=0

a = 4.5; b = 4; c = -138;
Δ = b2-4ac
Δ = 42-4·4.5·(-138)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-50}{2*4.5}=\frac{-54}{9}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+50}{2*4.5}=\frac{46}{9}
=5+1/9
$