x^2-4x=5/8

Solution for x^2-4x=5/8 equation:

x^2-4x=5/8

We move all terms to the left:

x^2-4x-(5/8)=0

We add all the numbers together, and all the variables

x^2-4x-(+5/8)=0

We get rid of parentheses

x^2-4x-5/8=0

We multiply all the terms by the denominator


x^2*8-4x*8-5=0

Wy multiply elements

8x^2-32x-5=0

a = 8; b = -32; c = -5;
Δ = b2-4ac
Δ = -322-4·8·(-5)
Δ = 1184
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:

$\sqrt{\Delta}=\sqrt{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{74}}{2*8}=\frac{32-4\sqrt{74}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{74}}{2*8}=\frac{32+4\sqrt{74}}{16}
$