7-x=0,5*x^2-2*x+3

Solution for 7-x=0,5*x^2-2*x+3 equation:

7-x=0.5x^2-2x+3

We move all terms to the left:

7-x-(0.5x^2-2x+3)=0

We add all the numbers together, and all the variables

-1x-(0.5x^2-2x+3)+7=0

We get rid of parentheses

-0.5x^2-1x+2x-3+7=0

We add all the numbers together, and all the variables

-0.5x^2+x+4=0

a = -0.5; b = 1; c = +4;
Δ = b2-4ac
Δ = 12-4·(-0.5)·4
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*-0.5}=\frac{-4}{-1}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*-0.5}=\frac{2}{-1}
=-2
$