2x^2-6x-7=-1/2

Solution for 2x^2-6x-7=-1/2 equation:

2x^2-6x-7=-1/2

We move all terms to the left:

2x^2-6x-7-(-1/2)=0

We get rid of parentheses

2x^2-6x-7+1/2=0

We multiply all the terms by the denominator


2x^2*2-6x*2+1-7*2=0

We add all the numbers together, and all the variables

2x^2*2-6x*2-13=0

Wy multiply elements

4x^2-12x-13=0

a = 4; b = -12; c = -13;
Δ = b2-4ac
Δ = -122-4·4·(-13)
Δ = 352
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{22}}{2*4}=\frac{12-4\sqrt{22}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{22}}{2*4}=\frac{12+4\sqrt{22}}{8}
$