4.5=1.25x^2+.0875x

Solution for 4.5=1.25x^2+.0875x equation:

4.5=1.25x^2+.0875x

We move all terms to the left:

4.5-(1.25x^2+.0875x)=0

We get rid of parentheses

-1.25x^2-.0875x+4.5=0

We add all the numbers together, and all the variables

-1.25x^2-0.0875x+4.5=0

a = -1.25; b = -0.0875; c = +4.5;
Δ = b2-4ac
Δ = -0.08752-4·(-1.25)·4.5
Δ = 22.50765625
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{-(-0.0875)-\sqrt{22.50765625}}{2*-1.25}=\frac{0.0875-\sqrt{22.50765625}}{-2.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.0875)+\sqrt{22.50765625}}{2*-1.25}=\frac{0.0875+\sqrt{22.50765625}}{-2.5}
$