3/5x+10=30x-180

Solution for 3/5x+10=30x-180 equation:

3/5x+10=30x-180

We move all terms to the left:

3/5x+10-(30x-180)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-30x+180+10=0

We multiply all the terms by the denominator


-30x*5x+180*5x+10*5x+3=0

Wy multiply elements

-150x^2+900x+50x+3=0

We add all the numbers together, and all the variables

-150x^2+950x+3=0

a = -150; b = 950; c = +3;
Δ = b2-4ac
Δ = 9502-4·(-150)·3
Δ = 904300
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:

$\sqrt{\Delta}=\sqrt{904300}=\sqrt{100*9043}=\sqrt{100}*\sqrt{9043}=10\sqrt{9043}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(950)-10\sqrt{9043}}{2*-150}=\frac{-950-10\sqrt{9043}}{-300}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(950)+10\sqrt{9043}}{2*-150}=\frac{-950+10\sqrt{9043}}{-300}
$