1/3(4x)+5x=20

Solution for 1/3(4x)+5x=20 equation:

1/3(4x)+5x=20

We move all terms to the left:

1/3(4x)+5x-(20)=0


Domain of the equation: 34x!=0

x!=0/34

x!=0

x∈R


We add all the numbers together, and all the variables

5x+1/34x-20=0

We multiply all the terms by the denominator


5x*34x-20*34x+1=0

Wy multiply elements

170x^2-680x+1=0

a = 170; b = -680; c = +1;
Δ = b2-4ac
Δ = -6802-4·170·1
Δ = 461720
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:

$\sqrt{\Delta}=\sqrt{461720}=\sqrt{4*115430}=\sqrt{4}*\sqrt{115430}=2\sqrt{115430}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-680)-2\sqrt{115430}}{2*170}=\frac{680-2\sqrt{115430}}{340}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-680)+2\sqrt{115430}}{2*170}=\frac{680+2\sqrt{115430}}{340}
$