4x^2-36x+7=28

Solution for 4x^2-36x+7=28 equation:

4x^2-36x+7=28

We move all terms to the left:

4x^2-36x+7-(28)=0

We add all the numbers together, and all the variables

4x^2-36x-21=0

a = 4; b = -36; c = -21;
Δ = b2-4ac
Δ = -362-4·4·(-21)
Δ = 1632
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:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{102}}{2*4}=\frac{36-4\sqrt{102}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{102}}{2*4}=\frac{36+4\sqrt{102}}{8}
$