1.5x^2+x=160

Solution for 1.5x^2+x=160 equation:

1.5x^2+x=160

We move all terms to the left:

1.5x^2+x-(160)=0

a = 1.5; b = 1; c = -160;
Δ = b2-4ac
Δ = 12-4·1.5·(-160)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-31}{2*1.5}=\frac{-32}{3}
=-10+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+31}{2*1.5}=\frac{30}{3}
=10
$