5x^2+1.5x=12

Solution for 5x^2+1.5x=12 equation:

5x^2+1.5x=12

We move all terms to the left:

5x^2+1.5x-(12)=0

a = 5; b = 1.5; c = -12;
Δ = b2-4ac
Δ = 1.52-4·5·(-12)
Δ = 242.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1.5)-\sqrt{242.25}}{2*5}=\frac{-1.5-\sqrt{242.25}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{242.25}}{2*5}=\frac{-1.5+\sqrt{242.25}}{10}
$