(x-7.75)+.25x(x-7.75)=8.50

Solution for (x-7.75)+.25x(x-7.75)=8.50 equation:

(x-7.75)+.25x(x-7.75)=8.50

We move all terms to the left:

(x-7.75)+.25x(x-7.75)-(8.50)=0

We add all the numbers together, and all the variables

(x-7.75)+.25x(x-7.75)-(8.5)=0

We add all the numbers together, and all the variables

(x-7.75)+.25x(x-7.75)-8.5=0

We multiply parentheses

x^2+(x-7.75)-7.75x-8.5=0

We get rid of parentheses

x^2+x-7.75x-7.75-8.5=0

We add all the numbers together, and all the variables

x^2-6.75x-16.25=0

a = 1; b = -6.75; c = -16.25;
Δ = b2-4ac
Δ = -6.752-4·1·(-16.25)
Δ = 110.5625
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{110.5625}}{2*1}=\frac{6.75-\sqrt{110.5625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6.75)+\sqrt{110.5625}}{2*1}=\frac{6.75+\sqrt{110.5625}}{2}
$