x(x+1)=x-25+74

Solution for x(x+1)=x-25+74 equation:

x(x+1)=x-25+74

We move all terms to the left:

x(x+1)-(x-25+74)=0

We add all the numbers together, and all the variables

x(x+1)-(x+49)=0

We multiply parentheses

x^2+x-(x+49)=0

We get rid of parentheses

x^2+x-x-49=0

We add all the numbers together, and all the variables

x^2-49=0

a = 1; b = 0; c = -49;
Δ = b2-4ac
Δ = 02-4·1·(-49)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14}{2*1}=\frac{14}{2}
=7
$