(-2x^2+7x-5)/(x-1)=0

Solution for (-2x^2+7x-5)/(x-1)=0 equation:

(-2x^2+7x-5)/(x-1)=0


Domain of the equation: (x-1)!=0

We move all terms containing x to the left, all other terms to the right

x!=1

x∈R


We multiply all the terms by the denominator


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

We get rid of parentheses

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

a = -2; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·(-2)·(-5)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3}{2*-2}=\frac{-4}{-4}
=1
$