X^2+3x(3-x/2)=10

Solution for X^2+3x(3-x/2)=10 equation:

X^2+3X(3-X/2)=10

We move all terms to the left:

X^2+3X(3-X/2)-(10)=0

We add all the numbers together, and all the variables

X^2+3X(-X/2+3)-10=0

We multiply parentheses

X^2-3X^2+9X-10=0

We add all the numbers together, and all the variables

-2X^2+9X-10=0

a = -2; b = 9; c = -10;
Δ = b2-4ac
Δ = 92-4·(-2)·(-10)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-1}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+1}{2*-2}=\frac{-8}{-4}
=+2
$