X(x+3)=2(x+10)+x+30

Solution for X(x+3)=2(x+10)+x+30 equation:

X(X+3)=2(X+10)+X+30

We move all terms to the left:

X(X+3)-(2(X+10)+X+30)=0

We multiply parentheses

X^2+3X-(2(X+10)+X+30)=0


We calculate terms in parentheses: -(2(X+10)+X+30), so:

2(X+10)+X+30

We add all the numbers together, and all the variables

X+2(X+10)+30

We multiply parentheses

X+2X+20+30

We add all the numbers together, and all the variables

3X+50

Back to the equation:

-(3X+50)


We get rid of parentheses

X^2+3X-3X-50=0

We add all the numbers together, and all the variables

X^2-50=0

a = 1; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·1·(-50)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{2}}{2*1}=\frac{0-10\sqrt{2}}{2}
=-\frac{10\sqrt{2}}{2}
=-5\sqrt{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2}}{2*1}=\frac{0+10\sqrt{2}}{2}
=\frac{10\sqrt{2}}{2}
=5\sqrt{2}
$