(x-5)(x-5)=3(x+5)

Solution for (x-5)(x-5)=3(x+5) equation:

(x-5)(x-5)=3(x+5)

We move all terms to the left:

(x-5)(x-5)-(3(x+5))=0

We multiply parentheses ..

(+x^2-5x-5x+25)-(3(x+5))=0


We calculate terms in parentheses: -(3(x+5)), so:

3(x+5)

We multiply parentheses

3x+15

Back to the equation:

-(3x+15)


We get rid of parentheses

x^2-5x-5x-3x+25-15=0

We add all the numbers together, and all the variables

x^2-13x+10=0

a = 1; b = -13; c = +10;
Δ = b2-4ac
Δ = -132-4·1·10
Δ = 129
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{-(-13)-\sqrt{129}}{2*1}=\frac{13-\sqrt{129}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{129}}{2*1}=\frac{13+\sqrt{129}}{2}
$