4(x-4);x=7

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

4(x-4)x=7

We move all terms to the left:

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

We multiply parentheses

4x^2-16x-7=0

a = 4; b = -16; c = -7;
Δ = b2-4ac
Δ = -162-4·4·(-7)
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{23}}{2*4}=\frac{16-4\sqrt{23}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{23}}{2*4}=\frac{16+4\sqrt{23}}{8}
$