4(x^2+21x-176)=0

Solution for 4(x^2+21x-176)=0 equation:

4(x^2+21x-176)=0

We multiply parentheses

4x^2+84x-704=0

a = 4; b = 84; c = -704;
Δ = b2-4ac
Δ = 842-4·4·(-704)
Δ = 18320
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:

$\sqrt{\Delta}=\sqrt{18320}=\sqrt{16*1145}=\sqrt{16}*\sqrt{1145}=4\sqrt{1145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{1145}}{2*4}=\frac{-84-4\sqrt{1145}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{1145}}{2*4}=\frac{-84+4\sqrt{1145}}{8}
$