X2+3x-1=(x+4)2

Solution for X2+3x-1=(x+4)2 equation:

X2+3X-1=(X+4)2

We move all terms to the left:

X2+3X-1-((X+4)2)=0

We add all the numbers together, and all the variables

X^2+3X-((X+4)2)-1=0


We calculate terms in parentheses: -((X+4)2), so:

(X+4)2

We multiply parentheses

2X+8

Back to the equation:

-(2X+8)


We get rid of parentheses

X^2+3X-2X-8-1=0

We add all the numbers together, and all the variables

X^2+X-9=0

a = 1; b = 1; c = -9;
Δ = b2-4ac
Δ = 12-4·1·(-9)
Δ = 37
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{37}}{2*1}=\frac{-1-\sqrt{37}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{37}}{2*1}=\frac{-1+\sqrt{37}}{2}
$