15(x+20)=-x+14+4/5x

Solution for 15(x+20)=-x+14+4/5x equation:

15(x+20)=-x+14+4/5x

We move all terms to the left:

15(x+20)-(-x+14+4/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

15(x+20)-(-1x+4/5x+14)=0

We multiply parentheses

15x-(-1x+4/5x+14)+300=0

We get rid of parentheses

15x+1x-4/5x-14+300=0

We multiply all the terms by the denominator


15x*5x+1x*5x-14*5x+300*5x-4=0

Wy multiply elements

75x^2+5x^2-70x+1500x-4=0

We add all the numbers together, and all the variables

80x^2+1430x-4=0

a = 80; b = 1430; c = -4;
Δ = b2-4ac
Δ = 14302-4·80·(-4)
Δ = 2046180
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:

$\sqrt{\Delta}=\sqrt{2046180}=\sqrt{4*511545}=\sqrt{4}*\sqrt{511545}=2\sqrt{511545}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1430)-2\sqrt{511545}}{2*80}=\frac{-1430-2\sqrt{511545}}{160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1430)+2\sqrt{511545}}{2*80}=\frac{-1430+2\sqrt{511545}}{160}
$