6=2x^2-5x

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

6=2x^2-5x

We move all terms to the left:

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

We get rid of parentheses

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

a = -2; b = 5; c = +6;
Δ = b2-4ac
Δ = 52-4·(-2)·6
Δ = 73
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{-(5)-\sqrt{73}}{2*-2}=\frac{-5-\sqrt{73}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{73}}{2*-2}=\frac{-5+\sqrt{73}}{-4}
$