0.25x^2+x=6

Solution for 0.25x^2+x=6 equation:

0.25x^2+x=6

We move all terms to the left:

0.25x^2+x-(6)=0

a = 0.25; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·0.25·(-6)
Δ = 7
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{-(1)-\sqrt{7}}{2*0.25}=\frac{-1-\sqrt{7}}{0.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{7}}{2*0.25}=\frac{-1+\sqrt{7}}{0.5}
$