x(5x+21)=2x^2-2x+8

Solution for x(5x+21)=2x^2-2x+8 equation:

x(5x+21)=2x^2-2x+8

We move all terms to the left:

x(5x+21)-(2x^2-2x+8)=0

We multiply parentheses

5x^2+21x-(2x^2-2x+8)=0

We get rid of parentheses

5x^2-2x^2+21x+2x-8=0

We add all the numbers together, and all the variables

3x^2+23x-8=0

a = 3; b = 23; c = -8;
Δ = b2-4ac
Δ = 232-4·3·(-8)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-25}{2*3}=\frac{-48}{6}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+25}{2*3}=\frac{2}{6}
=1/3
$