5x(x+1)-2(x-2)=21

Solution for 5x(x+1)-2(x-2)=21 equation:

5x(x+1)-2(x-2)=21

We move all terms to the left:

5x(x+1)-2(x-2)-(21)=0

We multiply parentheses

5x^2+5x-2x+4-21=0

We add all the numbers together, and all the variables

5x^2+3x-17=0

a = 5; b = 3; c = -17;
Δ = b2-4ac
Δ = 32-4·5·(-17)
Δ = 349
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{349}}{2*5}=\frac{-3-\sqrt{349}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{349}}{2*5}=\frac{-3+\sqrt{349}}{10}
$