x^2+x^2+14x+49=4x^2-28x+49

Solution for x^2+x^2+14x+49=4x^2-28x+49 equation:

x^2+x^2+14x+49=4x^2-28x+49

We move all terms to the left:

x^2+x^2+14x+49-(4x^2-28x+49)=0

We add all the numbers together, and all the variables

2x^2+14x-(4x^2-28x+49)+49=0

We get rid of parentheses

2x^2-4x^2+14x+28x-49+49=0

We add all the numbers together, and all the variables

-2x^2+42x=0

a = -2; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·(-2)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*-2}=\frac{-84}{-4}
=+21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*-2}=\frac{0}{-4}
=0
$