x(8x-59)=-21

Solution for x(8x-59)=-21 equation:

x(8x-59)=-21

We move all terms to the left:

x(8x-59)-(-21)=0

We add all the numbers together, and all the variables

x(8x-59)+21=0

We multiply parentheses

8x^2-59x+21=0

a = 8; b = -59; c = +21;
Δ = b2-4ac
Δ = -592-4·8·21
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-53}{2*8}=\frac{6}{16}
=3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+53}{2*8}=\frac{112}{16}
=7
$