1.5x^2+5x=84

Solution for 1.5x^2+5x=84 equation:

1.5x^2+5x=84

We move all terms to the left:

1.5x^2+5x-(84)=0

a = 1.5; b = 5; c = -84;
Δ = b2-4ac
Δ = 52-4·1.5·(-84)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-23}{2*1.5}=\frac{-28}{3}
=-9+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+23}{2*1.5}=\frac{18}{3}
=6
$