4x=-0.5x^2+3x+6

Solution for 4x=-0.5x^2+3x+6 equation:

4x=-0.5x^2+3x+6

We move all terms to the left:

4x-(-0.5x^2+3x+6)=0

We get rid of parentheses

0.5x^2-3x+4x-6=0

We add all the numbers together, and all the variables

0.5x^2+x-6=0

a = 0.5; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·0.5·(-6)
Δ = 13
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{13}}{2*0.5}=\frac{-1-\sqrt{13}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{13}}{2*0.5}=\frac{-1+\sqrt{13}}{1}
$