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

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

X(X+3)=5(2X+1)+4X

We move all terms to the left:

X(X+3)-(5(2X+1)+4X)=0

We multiply parentheses

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


We calculate terms in parentheses: -(5(2X+1)+4X), so:

5(2X+1)+4X

We add all the numbers together, and all the variables

4X+5(2X+1)

We multiply parentheses

4X+10X+5

We add all the numbers together, and all the variables

14X+5

Back to the equation:

-(14X+5)


We get rid of parentheses

X^2+3X-14X-5=0

We add all the numbers together, and all the variables

X^2-11X-5=0

a = 1; b = -11; c = -5;
Δ = b2-4ac
Δ = -112-4·1·(-5)
Δ = 141
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{-(-11)-\sqrt{141}}{2*1}=\frac{11-\sqrt{141}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{141}}{2*1}=\frac{11+\sqrt{141}}{2}
$