75^2=x^2+(x+51)

Solution for 75^2=x^2+(x+51) equation:

75^2=x^2+(x+51)

We move all terms to the left:

75^2-(x^2+(x+51))=0

We add all the numbers together, and all the variables

-(x^2+(x+51))+5625=0


We calculate terms in parentheses: -(x^2+(x+51)), so:

x^2+(x+51)

We get rid of parentheses

x^2+x+51

Back to the equation:

-(x^2+x+51)


We get rid of parentheses

-x^2-x-51+5625=0

We add all the numbers together, and all the variables

-1x^2-1x+5574=0

a = -1; b = -1; c = +5574;
Δ = b2-4ac
Δ = -12-4·(-1)·5574
Δ = 22297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{22297}}{2*-1}=\frac{1-\sqrt{22297}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{22297}}{2*-1}=\frac{1+\sqrt{22297}}{-2}
$