4/5x=3x+28

Solution for 4/5x=3x+28 equation:

4/5x=3x+28

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-3x-28=0

We multiply all the terms by the denominator


-3x*5x-28*5x+4=0

Wy multiply elements

-15x^2-140x+4=0

a = -15; b = -140; c = +4;
Δ = b2-4ac
Δ = -1402-4·(-15)·4
Δ = 19840
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:

$\sqrt{\Delta}=\sqrt{19840}=\sqrt{64*310}=\sqrt{64}*\sqrt{310}=8\sqrt{310}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-8\sqrt{310}}{2*-15}=\frac{140-8\sqrt{310}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+8\sqrt{310}}{2*-15}=\frac{140+8\sqrt{310}}{-30}
$