(25x^2-18)/(5x-4)=x

Solution for (25x^2-18)/(5x-4)=x equation:

(25x^2-18)/(5x-4)=x

We move all terms to the left:

(25x^2-18)/(5x-4)-(x)=0


Domain of the equation: (5x-4)!=0

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

5x!=4

x!=4/5

x!=4/5

x∈R


We add all the numbers together, and all the variables

-1x+(25x^2-18)/(5x-4)=0

We multiply all the terms by the denominator


-1x*(5x-4)+(25x^2-18)=0

We multiply parentheses

-5x^2+4x+(25x^2-18)=0

We get rid of parentheses

-5x^2+25x^2+4x-18=0

We add all the numbers together, and all the variables

20x^2+4x-18=0

a = 20; b = 4; c = -18;
Δ = b2-4ac
Δ = 42-4·20·(-18)
Δ = 1456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1456}=\sqrt{16*91}=\sqrt{16}*\sqrt{91}=4\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{91}}{2*20}=\frac{-4-4\sqrt{91}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{91}}{2*20}=\frac{-4+4\sqrt{91}}{40}
$