x+5=5/2x-4=3

Solution for x+5=5/2x-4=3 equation:

x+5=5/2x-4=3

We move all terms to the left:

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


Domain of the equation: 2x-4)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

2x^2+18x-5=0

a = 2; b = 18; c = -5;
Δ = b2-4ac
Δ = 182-4·2·(-5)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{91}}{2*2}=\frac{-18-2\sqrt{91}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{91}}{2*2}=\frac{-18+2\sqrt{91}}{4}
$