.25x+.75x(10-x)=3

Solution for .25x+.75x(10-x)=3 equation:

.25x+.75x(10-x)=3

We move all terms to the left:

.25x+.75x(10-x)-(3)=0

We add all the numbers together, and all the variables

.25x+.75x(-1x+10)-3=0

We multiply parentheses

-1x^2+.25x+10x-3=0

We add all the numbers together, and all the variables

-1x^2+10.25x-3=0

a = -1; b = 10.25; c = -3;
Δ = b2-4ac
Δ = 10.252-4·(-1)·(-3)
Δ = 93.0625
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{-(10.25)-\sqrt{93.0625}}{2*-1}=\frac{-10.25-\sqrt{93.0625}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10.25)+\sqrt{93.0625}}{2*-1}=\frac{-10.25+\sqrt{93.0625}}{-2}
$