3(x+5)-7x(x-2)=2x(6x+4)

Solution for 3(x+5)-7x(x-2)=2x(6x+4) equation:

3(x+5)-7x(x-2)=2x(6x+4)

We move all terms to the left:

3(x+5)-7x(x-2)-(2x(6x+4))=0

We multiply parentheses

-7x^2+3x+14x-(2x(6x+4))+15=0


We calculate terms in parentheses: -(2x(6x+4)), so:

2x(6x+4)

We multiply parentheses

12x^2+8x

Back to the equation:

-(12x^2+8x)


We add all the numbers together, and all the variables

-7x^2+17x-(12x^2+8x)+15=0

We get rid of parentheses

-7x^2-12x^2+17x-8x+15=0

We add all the numbers together, and all the variables

-19x^2+9x+15=0

a = -19; b = 9; c = +15;
Δ = b2-4ac
Δ = 92-4·(-19)·15
Δ = 1221
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{-(9)-\sqrt{1221}}{2*-19}=\frac{-9-\sqrt{1221}}{-38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{1221}}{2*-19}=\frac{-9+\sqrt{1221}}{-38}
$