4x2-28x+49=64

Solution for 4x2-28x+49=64 equation:

4x^2-28x+49=64

We move all terms to the left:

4x^2-28x+49-(64)=0

We add all the numbers together, and all the variables

4x^2-28x-15=0

a = 4; b = -28; c = -15;
Δ = b2-4ac
Δ = -282-4·4·(-15)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-32}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+32}{2*4}=\frac{60}{8}
=7+1/2
$