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

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

Wy multiply elements

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

We add all the numbers together, and all the variables

-2x^2+15x+8=0

a = -2; b = 15; c = +8;
Δ = b2-4ac
Δ = 152-4·(-2)·8
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-17}{2*-2}=\frac{-32}{-4}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+17}{2*-2}=\frac{2}{-4}
=-1/2
$