4x(x+6)=3(x+16)

Solution for 4x(x+6)=3(x+16) equation:

4x(x+6)=3(x+16)

We move all terms to the left:

4x(x+6)-(3(x+16))=0

We multiply parentheses

4x^2+24x-(3(x+16))=0


We calculate terms in parentheses: -(3(x+16)), so:

3(x+16)

We multiply parentheses

3x+48

Back to the equation:

-(3x+48)


We get rid of parentheses

4x^2+24x-3x-48=0

We add all the numbers together, and all the variables

4x^2+21x-48=0

a = 4; b = 21; c = -48;
Δ = b2-4ac
Δ = 212-4·4·(-48)
Δ = 1209
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{-(21)-\sqrt{1209}}{2*4}=\frac{-21-\sqrt{1209}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{1209}}{2*4}=\frac{-21+\sqrt{1209}}{8}
$