24x+42x=3(10x-1)x=2

Solution for 24x+42x=3(10x-1)x=2 equation:

24x+42x=3(10x-1)x=2

We move all terms to the left:

24x+42x-(3(10x-1)x)=0

We add all the numbers together, and all the variables

66x-(3(10x-1)x)=0


We calculate terms in parentheses: -(3(10x-1)x), so:

3(10x-1)x

We multiply parentheses

30x^2-3x

Back to the equation:

-(30x^2-3x)


We get rid of parentheses

-30x^2+66x+3x=0

We add all the numbers together, and all the variables

-30x^2+69x=0

a = -30; b = 69; c = 0;
Δ = b2-4ac
Δ = 692-4·(-30)·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-69}{2*-30}=\frac{-138}{-60}
=2+3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+69}{2*-30}=\frac{0}{-60}
=0
$