x^2+1.5x=1

Solution for x^2+1.5x=1 equation:

x^2+1.5x=1

We move all terms to the left:

x^2+1.5x-(1)=0

a = 1; b = 1.5; c = -1;
Δ = b2-4ac
Δ = 1.52-4·1·(-1)
Δ = 6.25
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{6.25}}{2*1}=\frac{-1.5-\sqrt{6.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{6.25}}{2*1}=\frac{-1.5+\sqrt{6.25}}{2}
$