5x+30=0.25x^2

Solution for 5x+30=0.25x^2 equation:

5x+30=0.25x^2

We move all terms to the left:

5x+30-(0.25x^2)=0

We get rid of parentheses

-0.25x^2+5x+30=0

a = -0.25; b = 5; c = +30;
Δ = b2-4ac
Δ = 52-4·(-0.25)·30
Δ = 55
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{-(5)-\sqrt{55}}{2*-0.25}=\frac{-5-\sqrt{55}}{-0.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{55}}{2*-0.25}=\frac{-5+\sqrt{55}}{-0.5}
$