(10x-3)(3x+1)=6x

Solution for (10x-3)(3x+1)=6x equation:

(10x-3)(3x+1)=6x

We move all terms to the left:

(10x-3)(3x+1)-(6x)=0

We add all the numbers together, and all the variables

-6x+(10x-3)(3x+1)=0

We multiply parentheses ..

(+30x^2+10x-9x-3)-6x=0

We get rid of parentheses

30x^2+10x-9x-6x-3=0

We add all the numbers together, and all the variables

30x^2-5x-3=0

a = 30; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·30·(-3)
Δ = 385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{385}}{2*30}=\frac{5-\sqrt{385}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{385}}{2*30}=\frac{5+\sqrt{385}}{60}
$