-5x^2+2.5x+6=2x

Solution for -5x^2+2.5x+6=2x equation:

-5x^2+2.5x+6=2x

We move all terms to the left:

-5x^2+2.5x+6-(2x)=0

We add all the numbers together, and all the variables

-5x^2+0.5x+6=0

a = -5; b = 0.5; c = +6;
Δ = b2-4ac
Δ = 0.52-4·(-5)·6
Δ = 120.25
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{-(0.5)-\sqrt{120.25}}{2*-5}=\frac{-0.5-\sqrt{120.25}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{120.25}}{2*-5}=\frac{-0.5+\sqrt{120.25}}{-10}
$