x(4x+3)=21

Solution for x(4x+3)=21 equation:

x(4x+3)=21

We move all terms to the left:

x(4x+3)-(21)=0

We multiply parentheses

4x^2+3x-21=0

a = 4; b = 3; c = -21;
Δ = b2-4ac
Δ = 32-4·4·(-21)
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{345}}{2*4}=\frac{-3-\sqrt{345}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{345}}{2*4}=\frac{-3+\sqrt{345}}{8}
$