x*x+2-3/4=(5*6)+1

Solution for x*x+2-3/4=(5*6)+1 equation:

x*x+2-3/4=(5*6)+1

We move all terms to the left:

x*x+2-3/4-((5*6)+1)=0

We add all the numbers together, and all the variables

x*x+2-3/4-(30+1)=0

We add all the numbers together, and all the variables

x*x-29-3/4=0

Wy multiply elements

x^2-29-3/4=0

We multiply all the terms by the denominator


x^2*4-3-29*4=0

We add all the numbers together, and all the variables

x^2*4-119=0

Wy multiply elements

4x^2-119=0

a = 4; b = 0; c = -119;
Δ = b2-4ac
Δ = 02-4·4·(-119)
Δ = 1904
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:

$\sqrt{\Delta}=\sqrt{1904}=\sqrt{16*119}=\sqrt{16}*\sqrt{119}=4\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{119}}{2*4}=\frac{0-4\sqrt{119}}{8}
=-\frac{4\sqrt{119}}{8}
=-\frac{\sqrt{119}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{119}}{2*4}=\frac{0+4\sqrt{119}}{8}
=\frac{4\sqrt{119}}{8}
=\frac{\sqrt{119}}{2}
$