4+7x-x^2=x/2

Solution for 4+7x-x^2=x/2 equation:

4+7x-x^2=x/2

We move all terms to the left:

4+7x-x^2-(x/2)=0

We add all the numbers together, and all the variables

-x^2+7x-(+x/2)+4=0

We add all the numbers together, and all the variables

-1x^2+7x-(+x/2)+4=0

We get rid of parentheses

-1x^2+7x-x/2+4=0

We multiply all the terms by the denominator


-1x^2*2+7x*2-x+4*2=0

We add all the numbers together, and all the variables

-1x^2*2-1x+7x*2+8=0

Wy multiply elements

-2x^2-1x+14x+8=0

We add all the numbers together, and all the variables

-2x^2+13x+8=0

a = -2; b = 13; c = +8;
Δ = b2-4ac
Δ = 132-4·(-2)·8
Δ = 233
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{-(13)-\sqrt{233}}{2*-2}=\frac{-13-\sqrt{233}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{233}}{2*-2}=\frac{-13+\sqrt{233}}{-4}
$