5x+4=5/2x-5

Solution for 5x+4=5/2x-5 equation:

5x+4=5/2x-5

We move all terms to the left:

5x+4-(5/2x-5)=0


Domain of the equation: 2x-5)!=0

x∈R


We get rid of parentheses

5x-5/2x+5+4=0

We multiply all the terms by the denominator


5x*2x+5*2x+4*2x-5=0

Wy multiply elements

10x^2+10x+8x-5=0

We add all the numbers together, and all the variables

10x^2+18x-5=0

a = 10; b = 18; c = -5;
Δ = b2-4ac
Δ = 182-4·10·(-5)
Δ = 524
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:

$\sqrt{\Delta}=\sqrt{524}=\sqrt{4*131}=\sqrt{4}*\sqrt{131}=2\sqrt{131}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{131}}{2*10}=\frac{-18-2\sqrt{131}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{131}}{2*10}=\frac{-18+2\sqrt{131}}{20}
$