x^2+5x/2=21

Solution for x^2+5x/2=21 equation:

x^2+5x/2=21

We move all terms to the left:

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x^2*2+5x-42=0

Wy multiply elements

2x^2+5x-42=0

a = 2; b = 5; c = -42;
Δ = b2-4ac
Δ = 52-4·2·(-42)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*2}=\frac{14}{4}
=3+1/2
$