j^2-j-1=23/4

Solution for j^2-j-1=23/4 equation:

j^2-j-1=23/4

We move all terms to the left:

j^2-j-1-(23/4)=0

We add all the numbers together, and all the variables

j^2-j-1-(+23/4)=0

We add all the numbers together, and all the variables

j^2-1j-1-(+23/4)=0

We get rid of parentheses

j^2-1j-1-23/4=0

We multiply all the terms by the denominator


j^2*4-1j*4-23-1*4=0

We add all the numbers together, and all the variables

j^2*4-1j*4-27=0

Wy multiply elements

4j^2-4j-27=0

a = 4; b = -4; c = -27;
Δ = b2-4ac
Δ = -42-4·4·(-27)
Δ = 448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{7}}{2*4}=\frac{4-8\sqrt{7}}{8}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{7}}{2*4}=\frac{4+8\sqrt{7}}{8}
$