3/5x-6=7x-26

Solution for 3/5x-6=7x-26 equation:

3/5x-6=7x-26

We move all terms to the left:

3/5x-6-(7x-26)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-7x+26-6=0

We multiply all the terms by the denominator


-7x*5x+26*5x-6*5x+3=0

Wy multiply elements

-35x^2+130x-30x+3=0

We add all the numbers together, and all the variables

-35x^2+100x+3=0

a = -35; b = 100; c = +3;
Δ = b2-4ac
Δ = 1002-4·(-35)·3
Δ = 10420
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:

$\sqrt{\Delta}=\sqrt{10420}=\sqrt{4*2605}=\sqrt{4}*\sqrt{2605}=2\sqrt{2605}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-2\sqrt{2605}}{2*-35}=\frac{-100-2\sqrt{2605}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+2\sqrt{2605}}{2*-35}=\frac{-100+2\sqrt{2605}}{-70}
$