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

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

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

We move all terms to the left:

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

We multiply parentheses

5x-(4x(x+3))+10=0


We calculate terms in parentheses: -(4x(x+3)), so:

4x(x+3)

We multiply parentheses

4x^2+12x

Back to the equation:

-(4x^2+12x)


We get rid of parentheses

-4x^2+5x-12x+10=0

We add all the numbers together, and all the variables

-4x^2-7x+10=0

a = -4; b = -7; c = +10;
Δ = b2-4ac
Δ = -72-4·(-4)·10
Δ = 209
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{-(-7)-\sqrt{209}}{2*-4}=\frac{7-\sqrt{209}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{209}}{2*-4}=\frac{7+\sqrt{209}}{-8}
$