-2x^2=5x-7

Solution for -2x^2=5x-7 equation:

-2x^2=5x-7

We move all terms to the left:

-2x^2-(5x-7)=0

We get rid of parentheses

-2x^2-5x+7=0

a = -2; b = -5; c = +7;
Δ = b2-4ac
Δ = -52-4·(-2)·7
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-9}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+9}{2*-2}=\frac{14}{-4}
=-3+1/2
$