2x^2+x=21.25

Solution for 2x^2+x=21.25 equation:

2x^2+x=21.25

We move all terms to the left:

2x^2+x-(21.25)=0

We add all the numbers together, and all the variables

2x^2+x-21.25=0

a = 2; b = 1; c = -21.25;
Δ = b2-4ac
Δ = 12-4·2·(-21.25)
Δ = 171
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{171}=\sqrt{9*19}=\sqrt{9}*\sqrt{19}=3\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{19}}{2*2}=\frac{-1-3\sqrt{19}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{19}}{2*2}=\frac{-1+3\sqrt{19}}{4}
$