10=1.5x+x^2

Solution for 10=1.5x+x^2 equation:

10=1.5x+x^2

We move all terms to the left:

10-(1.5x+x^2)=0

We get rid of parentheses

-x^2-1.5x+10=0

We add all the numbers together, and all the variables

-1x^2-1.5x+10=0

a = -1; b = -1.5; c = +10;
Δ = b2-4ac
Δ = -1.52-4·(-1)·10
Δ = 42.25
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{42.25}}{2*-1}=\frac{1.5-\sqrt{42.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{42.25}}{2*-1}=\frac{1.5+\sqrt{42.25}}{-2}
$