4x(x-4)=35

Solution for 4x(x-4)=35 equation:

4x(x-4)=35

We move all terms to the left:

4x(x-4)-(35)=0

We multiply parentheses

4x^2-16x-35=0

a = 4; b = -16; c = -35;
Δ = b2-4ac
Δ = -162-4·4·(-35)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{51}}{2*4}=\frac{16-4\sqrt{51}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{51}}{2*4}=\frac{16+4\sqrt{51}}{8}
$