x(4x-23)=-21

Solution for x(4x-23)=-21 equation:

x(4x-23)=-21

We move all terms to the left:

x(4x-23)-(-21)=0

We add all the numbers together, and all the variables

x(4x-23)+21=0

We multiply parentheses

4x^2-23x+21=0

a = 4; b = -23; c = +21;
Δ = b2-4ac
Δ = -232-4·4·21
Δ = 193
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{-(-23)-\sqrt{193}}{2*4}=\frac{23-\sqrt{193}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{193}}{2*4}=\frac{23+\sqrt{193}}{8}
$