-3.5x+7.5=0.25x^2+5x-3.2

Solution for -3.5x+7.5=0.25x^2+5x-3.2 equation:

-3.5x+7.5=0.25x^2+5x-3.2

We move all terms to the left:

-3.5x+7.5-(0.25x^2+5x-3.2)=0

We get rid of parentheses

-0.25x^2-3.5x-5x+3.2+7.5=0

We add all the numbers together, and all the variables

-0.25x^2-8.5x+10.7=0

a = -0.25; b = -8.5; c = +10.7;
Δ = b2-4ac
Δ = -8.52-4·(-0.25)·10.7
Δ = 82.95
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{-(-8.5)-\sqrt{82.95}}{2*-0.25}=\frac{8.5-\sqrt{82.95}}{-0.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.5)+\sqrt{82.95}}{2*-0.25}=\frac{8.5+\sqrt{82.95}}{-0.5}
$