2/3x-75=5x-7

Solution for 2/3x-75=5x-7 equation:

2/3x-75=5x-7

We move all terms to the left:

2/3x-75-(5x-7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-5x+7-75=0

We multiply all the terms by the denominator


-5x*3x+7*3x-75*3x+2=0

Wy multiply elements

-15x^2+21x-225x+2=0

We add all the numbers together, and all the variables

-15x^2-204x+2=0

a = -15; b = -204; c = +2;
Δ = b2-4ac
Δ = -2042-4·(-15)·2
Δ = 41736
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:

$\sqrt{\Delta}=\sqrt{41736}=\sqrt{4*10434}=\sqrt{4}*\sqrt{10434}=2\sqrt{10434}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-2\sqrt{10434}}{2*-15}=\frac{204-2\sqrt{10434}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+2\sqrt{10434}}{2*-15}=\frac{204+2\sqrt{10434}}{-30}
$