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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

4(x+2)

We multiply parentheses

4x+8

Back to the equation:

-(4x+8)


We get rid of parentheses

5x^2+5x-4x-8=0

We add all the numbers together, and all the variables

5x^2+x-8=0

a = 5; b = 1; c = -8;
Δ = b2-4ac
Δ = 12-4·5·(-8)
Δ = 161
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{161}}{2*5}=\frac{-1-\sqrt{161}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{161}}{2*5}=\frac{-1+\sqrt{161}}{10}
$