2.5x+1.5=2x^2-5

Solution for 2.5x+1.5=2x^2-5 equation:

2.5x+1.5=2x^2-5

We move all terms to the left:

2.5x+1.5-(2x^2-5)=0

We get rid of parentheses

-2x^2+2.5x+5+1.5=0

We add all the numbers together, and all the variables

-2x^2+2.5x+6.5=0

a = -2; b = 2.5; c = +6.5;
Δ = b2-4ac
Δ = 2.52-4·(-2)·6.5
Δ = 58.25
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{-(2.5)-\sqrt{58.25}}{2*-2}=\frac{-2.5-\sqrt{58.25}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{58.25}}{2*-2}=\frac{-2.5+\sqrt{58.25}}{-4}
$