4/5x+7=3x-19

Solution for 4/5x+7=3x-19 equation:

4/5x+7=3x-19

We move all terms to the left:

4/5x+7-(3x-19)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-3x+19+7=0

We multiply all the terms by the denominator


-3x*5x+19*5x+7*5x+4=0

Wy multiply elements

-15x^2+95x+35x+4=0

We add all the numbers together, and all the variables

-15x^2+130x+4=0

a = -15; b = 130; c = +4;
Δ = b2-4ac
Δ = 1302-4·(-15)·4
Δ = 17140
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:

$\sqrt{\Delta}=\sqrt{17140}=\sqrt{4*4285}=\sqrt{4}*\sqrt{4285}=2\sqrt{4285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-2\sqrt{4285}}{2*-15}=\frac{-130-2\sqrt{4285}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+2\sqrt{4285}}{2*-15}=\frac{-130+2\sqrt{4285}}{-30}
$