2/5x+4=-3x+21

Solution for 2/5x+4=-3x+21 equation:

2/5x+4=-3x+21

We move all terms to the left:

2/5x+4-(-3x+21)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x+3x-21+4=0

We multiply all the terms by the denominator


3x*5x-21*5x+4*5x+2=0

Wy multiply elements

15x^2-105x+20x+2=0

We add all the numbers together, and all the variables

15x^2-85x+2=0

a = 15; b = -85; c = +2;
Δ = b2-4ac
Δ = -852-4·15·2
Δ = 7105
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:

$\sqrt{\Delta}=\sqrt{7105}=\sqrt{49*145}=\sqrt{49}*\sqrt{145}=7\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-7\sqrt{145}}{2*15}=\frac{85-7\sqrt{145}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+7\sqrt{145}}{2*15}=\frac{85+7\sqrt{145}}{30}
$