2x^2+3x-5=4.5

Solution for 2x^2+3x-5=4.5 equation:

2x^2+3x-5=4.5

We move all terms to the left:

2x^2+3x-5-(4.5)=0

We add all the numbers together, and all the variables

2x^2+3x-9.5=0

a = 2; b = 3; c = -9.5;
Δ = b2-4ac
Δ = 32-4·2·(-9.5)
Δ = 85
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{-(3)-\sqrt{85}}{2*2}=\frac{-3-\sqrt{85}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{85}}{2*2}=\frac{-3+\sqrt{85}}{4}
$