x2-x-3-53/4=0

Solution for x2-x-3-53/4=0 equation:

x2-x-3-53/4=0

We add all the numbers together, and all the variables

x^2-1x-3-53/4=0

We multiply all the terms by the denominator


x^2*4-1x*4-53-3*4=0

We add all the numbers together, and all the variables

x^2*4-1x*4-65=0

Wy multiply elements

4x^2-4x-65=0

a = 4; b = -4; c = -65;
Δ = b2-4ac
Δ = -42-4·4·(-65)
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{66}}{2*4}=\frac{4-4\sqrt{66}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{66}}{2*4}=\frac{4+4\sqrt{66}}{8}
$