(X+5)(x+5)=10x+74

Solution for (X+5)(x+5)=10x+74 equation:

(X+5)(X+5)=10X+74

We move all terms to the left:

(X+5)(X+5)-(10X+74)=0

We get rid of parentheses

(X+5)(X+5)-10X-74=0

We multiply parentheses ..

(+X^2+5X+5X+25)-10X-74=0

We get rid of parentheses

X^2+5X+5X-10X+25-74=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
$