0.25x+4=7x-x^2

Solution for 0.25x+4=7x-x^2 equation:

0.25x+4=7x-x^2

We move all terms to the left:

0.25x+4-(7x-x^2)=0

We get rid of parentheses

x^2-7x+0.25x+4=0

We add all the numbers together, and all the variables

x^2-6.75x+4=0

a = 1; b = -6.75; c = +4;
Δ = b2-4ac
Δ = -6.752-4·1·4
Δ = 29.5625
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{-(-6.75)-\sqrt{29.5625}}{2*1}=\frac{6.75-\sqrt{29.5625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6.75)+\sqrt{29.5625}}{2*1}=\frac{6.75+\sqrt{29.5625}}{2}
$