x^2=4x-9/4=0

Solution for x^2=4x-9/4=0 equation:

x^2=4x-9/4=0

We move all terms to the left:

x^2-(4x-9/4)=0

We add all the numbers together, and all the variables

x^2-(+4x-9/4)=0

We get rid of parentheses

x^2-4x+9/4=0

We multiply all the terms by the denominator


x^2*4-4x*4+9=0

Wy multiply elements

4x^2-16x+9=0

a = 4; b = -16; c = +9;
Δ = b2-4ac
Δ = -162-4·4·9
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{7}}{2*4}=\frac{16-4\sqrt{7}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{7}}{2*4}=\frac{16+4\sqrt{7}}{8}
$