35=3/2x+x

Solution for 35=3/2x+x equation:

35=3/2x+x

We move all terms to the left:

35-(3/2x+x)=0


Domain of the equation: 2x+x)!=0

x∈R


We add all the numbers together, and all the variables

-(+x+3/2x)+35=0

We get rid of parentheses

-x-3/2x+35=0

We multiply all the terms by the denominator


-x*2x+35*2x-3=0

Wy multiply elements

-2x^2+70x-3=0

a = -2; b = 70; c = -3;
Δ = b2-4ac
Δ = 702-4·(-2)·(-3)
Δ = 4876
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:

$\sqrt{\Delta}=\sqrt{4876}=\sqrt{4*1219}=\sqrt{4}*\sqrt{1219}=2\sqrt{1219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{1219}}{2*-2}=\frac{-70-2\sqrt{1219}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{1219}}{2*-2}=\frac{-70+2\sqrt{1219}}{-4}
$