4(x^2+9x-42)=0

Solution for 4(x^2+9x-42)=0 equation:

4(x^2+9x-42)=0

We multiply parentheses

4x^2+36x-168=0

a = 4; b = 36; c = -168;
Δ = b2-4ac
Δ = 362-4·4·(-168)
Δ = 3984
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:

$\sqrt{\Delta}=\sqrt{3984}=\sqrt{16*249}=\sqrt{16}*\sqrt{249}=4\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{249}}{2*4}=\frac{-36-4\sqrt{249}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{249}}{2*4}=\frac{-36+4\sqrt{249}}{8}
$