x(x+3)+8=3(x-1)+15

Solution for x(x+3)+8=3(x-1)+15 equation:

x(x+3)+8=3(x-1)+15

We move all terms to the left:

x(x+3)+8-(3(x-1)+15)=0

We multiply parentheses

x^2+3x-(3(x-1)+15)+8=0


We calculate terms in parentheses: -(3(x-1)+15), so:

3(x-1)+15

We multiply parentheses

3x-3+15

We add all the numbers together, and all the variables

3x+12

Back to the equation:

-(3x+12)


We get rid of parentheses

x^2+3x-3x-12+8=0

We add all the numbers together, and all the variables

x^2-4=0

a = 1; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·1·(-4)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*1}=\frac{4}{2}
=2
$