5(x+1)+4x^2+4x+3=3(x+3)

Solution for 5(x+1)+4x^2+4x+3=3(x+3) equation:

5(x+1)+4x^2+4x+3=3(x+3)

We move all terms to the left:

5(x+1)+4x^2+4x+3-(3(x+3))=0

We add all the numbers together, and all the variables

4x^2+4x+5(x+1)-(3(x+3))+3=0

We multiply parentheses

4x^2+4x+5x-(3(x+3))+5+3=0


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

3(x+3)

We multiply parentheses

3x+9

Back to the equation:

-(3x+9)


We add all the numbers together, and all the variables

4x^2+9x-(3x+9)+8=0

We get rid of parentheses

4x^2+9x-3x-9+8=0

We add all the numbers together, and all the variables

4x^2+6x-1=0

a = 4; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·4·(-1)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{13}}{2*4}=\frac{-6-2\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{13}}{2*4}=\frac{-6+2\sqrt{13}}{8}
$