-x2+3x-2=-3/4

Solution for -x2+3x-2=-3/4 equation:

-x2+3x-2=-3/4

We move all terms to the left:

-x2+3x-2-(-3/4)=0

We add all the numbers together, and all the variables

-1x^2+3x-2-(-3/4)=0

We get rid of parentheses

-1x^2+3x-2+3/4=0

We multiply all the terms by the denominator


-1x^2*4+3x*4+3-2*4=0

We add all the numbers together, and all the variables

-1x^2*4+3x*4-5=0

Wy multiply elements

-4x^2+12x-5=0

a = -4; b = 12; c = -5;
Δ = b2-4ac
Δ = 122-4·(-4)·(-5)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8}{2*-4}=\frac{-20}{-8}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8}{2*-4}=\frac{-4}{-8}
=1/2
$