x(4x+3)=189

Solution for x(4x+3)=189 equation:

x(4x+3)=189

We move all terms to the left:

x(4x+3)-(189)=0

We multiply parentheses

4x^2+3x-189=0

a = 4; b = 3; c = -189;
Δ = b2-4ac
Δ = 32-4·4·(-189)
Δ = 3033
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:

$\sqrt{\Delta}=\sqrt{3033}=\sqrt{9*337}=\sqrt{9}*\sqrt{337}=3\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{337}}{2*4}=\frac{-3-3\sqrt{337}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{337}}{2*4}=\frac{-3+3\sqrt{337}}{8}
$