3x(4x+14)=10x-2x(x-7)

Solution for 3x(4x+14)=10x-2x(x-7) equation:

3x(4x+14)=10x-2x(x-7)

We move all terms to the left:

3x(4x+14)-(10x-2x(x-7))=0

We multiply parentheses

12x^2+42x-(10x-2x(x-7))=0


We calculate terms in parentheses: -(10x-2x(x-7)), so:

10x-2x(x-7)

We multiply parentheses

-2x^2+10x+14x

We add all the numbers together, and all the variables

-2x^2+24x

Back to the equation:

-(-2x^2+24x)


We get rid of parentheses

12x^2+2x^2-24x+42x=0

We add all the numbers together, and all the variables

14x^2+18x=0

a = 14; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·14·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*14}=\frac{-36}{28}
=-1+2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*14}=\frac{0}{28}
=0
$