2x^2=2.5x+1.5

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

2x^2=2.5x+1.5

We move all terms to the left:

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

We get rid of parentheses

2x^2-2.5x-1.5=0

a = 2; b = -2.5; c = -1.5;
Δ = b2-4ac
Δ = -2.52-4·2·(-1.5)
Δ = 18.25
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{18.25}}{2*2}=\frac{2.5-\sqrt{18.25}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.5)+\sqrt{18.25}}{2*2}=\frac{2.5+\sqrt{18.25}}{4}
$