3(1/2x+4)-10=1/5x+28

Solution for 3(1/2x+4)-10=1/5x+28 equation:

3(1/2x+4)-10=1/5x+28

We move all terms to the left:

3(1/2x+4)-10-(1/5x+28)=0


Domain of the equation: 2x+4)!=0

x∈R



Domain of the equation: 5x+28)!=0

x∈R


We multiply parentheses

3x-(1/5x+28)+12-10=0

We get rid of parentheses

3x-1/5x-28+12-10=0

We multiply all the terms by the denominator


3x*5x-28*5x+12*5x-10*5x-1=0

Wy multiply elements

15x^2-140x+60x-50x-1=0

We add all the numbers together, and all the variables

15x^2-130x-1=0

a = 15; b = -130; c = -1;
Δ = b2-4ac
Δ = -1302-4·15·(-1)
Δ = 16960
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:

$\sqrt{\Delta}=\sqrt{16960}=\sqrt{64*265}=\sqrt{64}*\sqrt{265}=8\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-8\sqrt{265}}{2*15}=\frac{130-8\sqrt{265}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+8\sqrt{265}}{2*15}=\frac{130+8\sqrt{265}}{30}
$