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

Solution for X^2-x-(7/4)=0 equation:

X^2-X-(7/4)=0

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

X^2-1X-7/4=0

We multiply all the terms by the denominator


X^2*4-1X*4-7=0

Wy multiply elements

4X^2-4X-7=0

a = 4; b = -4; c = -7;
Δ = b2-4ac
Δ = -42-4·4·(-7)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{2}}{2*4}=\frac{4-8\sqrt{2}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{2}}{2*4}=\frac{4+8\sqrt{2}}{8}
$