4x(x+5)=12

Solution for 4x(x+5)=12 equation:

4x(x+5)=12

We move all terms to the left:

4x(x+5)-(12)=0

We multiply parentheses

4x^2+20x-12=0

a = 4; b = 20; c = -12;
Δ = b2-4ac
Δ = 202-4·4·(-12)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{37}}{2*4}=\frac{-20-4\sqrt{37}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{37}}{2*4}=\frac{-20+4\sqrt{37}}{8}
$