4x(x-7)=-8

Solution for 4x(x-7)=-8 equation:

4x(x-7)=-8

We move all terms to the left:

4x(x-7)-(-8)=0

We add all the numbers together, and all the variables

4x(x-7)+8=0

We multiply parentheses

4x^2-28x+8=0

a = 4; b = -28; c = +8;
Δ = b2-4ac
Δ = -282-4·4·8
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{41}}{2*4}=\frac{28-4\sqrt{41}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{41}}{2*4}=\frac{28+4\sqrt{41}}{8}
$