4x(x-3)=196

Solution for 4x(x-3)=196 equation:

4x(x-3)=196

We move all terms to the left:

4x(x-3)-(196)=0

We multiply parentheses

4x^2-12x-196=0

a = 4; b = -12; c = -196;
Δ = b2-4ac
Δ = -122-4·4·(-196)
Δ = 3280
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:

$\sqrt{\Delta}=\sqrt{3280}=\sqrt{16*205}=\sqrt{16}*\sqrt{205}=4\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{205}}{2*4}=\frac{12-4\sqrt{205}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{205}}{2*4}=\frac{12+4\sqrt{205}}{8}
$