t^2+t=1.5

Solution for t^2+t=1.5 equation:

t^2+t=1.5

We move all terms to the left:

t^2+t-(1.5)=0

We add all the numbers together, and all the variables

t^2+t-1.5=0

a = 1; b = 1; c = -1.5;
Δ = b2-4ac
Δ = 12-4·1·(-1.5)
Δ = 7
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{7}}{2*1}=\frac{-1-\sqrt{7}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{7}}{2*1}=\frac{-1+\sqrt{7}}{2}
$