0.25x^2=x+7

Solution for 0.25x^2=x+7 equation:

0.25x^2=x+7

We move all terms to the left:

0.25x^2-(x+7)=0

We get rid of parentheses

0.25x^2-x-7=0

We add all the numbers together, and all the variables

0.25x^2-1x-7=0

a = 0.25; b = -1; c = -7;
Δ = b2-4ac
Δ = -12-4·0.25·(-7)
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-2\sqrt{2}}{2*0.25}=\frac{1-2\sqrt{2}}{0.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+2\sqrt{2}}{2*0.25}=\frac{1+2\sqrt{2}}{0.5}
$