20+3x=x^2/2

Solution for 20+3x=x^2/2 equation:

20+3x=x^2/2

We move all terms to the left:

20+3x-(x^2/2)=0

We get rid of parentheses

-x^2/2+3x+20=0

We multiply all the terms by the denominator


-x^2+3x*2+20*2=0

We add all the numbers together, and all the variables

-1x^2+3x*2+40=0

Wy multiply elements

-1x^2+6x+40=0

a = -1; b = 6; c = +40;
Δ = b2-4ac
Δ = 62-4·(-1)·40
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*-1}=\frac{8}{-2}
=-4
$