1.5^2=x^2+x^

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

1.5^2=x^2+x^

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(x^2+x^)+2.25=0

We get rid of parentheses

-x^2-x^+2.25=0

We add all the numbers together, and all the variables

-1x^2-1x+2.25=0

a = -1; b = -1; c = +2.25;
Δ = b2-4ac
Δ = -12-4·(-1)·2.25
Δ = 10
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)-\sqrt{10}}{2*-1}=\frac{1-\sqrt{10}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{10}}{2*-1}=\frac{1+\sqrt{10}}{-2}
$