x(x+3/4)=1/4

Solution for x(x+3/4)=1/4 equation:

x(x+3/4)=1/4

We move all terms to the left:

x(x+3/4)-(1/4)=0

We add all the numbers together, and all the variables

x(+x+3/4)-(+1/4)=0

We multiply parentheses

x^2+3x^2-(+1/4)=0

We get rid of parentheses

x^2+3x^2-1/4=0

We multiply all the terms by the denominator


x^2*4+3x^2*4-1=0

Wy multiply elements

4x^2+12x^2-1=0

We add all the numbers together, and all the variables

16x^2-1=0

a = 16; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·16·(-1)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*16}=\frac{-8}{32}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*16}=\frac{8}{32}
=1/4
$