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x2-3x+5=(x+5)2

We move all terms to the left:

x2-3x+5-((x+5)2)=0

We add all the numbers together, and all the variables

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

We calculate terms in parentheses: -((x+5)2), so:We get rid of parentheses

(x+5)2

We multiply parentheses

2x+10

Back to the equation:

-(2x+10)

x^2-3x-2x-10+5=0

We add all the numbers together, and all the variables

x^2-5x-5=0

a = 1; b = -5; c = -5;

Δ = b^{2}-4ac

Δ = -5^{2}-4·1·(-5)

Δ = 45

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}$

The end solution:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{5}}{2*1}=\frac{5-3\sqrt{5}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{5}}{2*1}=\frac{5+3\sqrt{5}}{2} $

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