5x+26=4-3/2x

Solution for 5x+26=4-3/2x equation:

5x+26=4-3/2x

We move all terms to the left:

5x+26-(4-3/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(-3/2x+4)+26=0

We get rid of parentheses

5x+3/2x-4+26=0

We multiply all the terms by the denominator


5x*2x-4*2x+26*2x+3=0

Wy multiply elements

10x^2-8x+52x+3=0

We add all the numbers together, and all the variables

10x^2+44x+3=0

a = 10; b = 44; c = +3;
Δ = b2-4ac
Δ = 442-4·10·3
Δ = 1816
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:

$\sqrt{\Delta}=\sqrt{1816}=\sqrt{4*454}=\sqrt{4}*\sqrt{454}=2\sqrt{454}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-2\sqrt{454}}{2*10}=\frac{-44-2\sqrt{454}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+2\sqrt{454}}{2*10}=\frac{-44+2\sqrt{454}}{20}
$