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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x^2*2+7x*2=0

Wy multiply elements

2x^2+14x=0

a = 2; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·2·0
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{-(14)-14}{2*2}=\frac{-28}{4}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*2}=\frac{0}{4}
=0
$