3(4x+7)=(4x-2)7x+15=3(3x-7)

Solution for 3(4x+7)=(4x-2)7x+15=3(3x-7) equation:

3(4x+7)=(4x-2)7x+15=3(3x-7)

We move all terms to the left:

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

We multiply parentheses

12x-((4x-2)7x+15)+21=0


We calculate terms in parentheses: -((4x-2)7x+15), so:

(4x-2)7x+15

We multiply parentheses

28x^2-14x+15

Back to the equation:

-(28x^2-14x+15)


We get rid of parentheses

-28x^2+12x+14x-15+21=0

We add all the numbers together, and all the variables

-28x^2+26x+6=0

a = -28; b = 26; c = +6;
Δ = b2-4ac
Δ = 262-4·(-28)·6
Δ = 1348
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:

$\sqrt{\Delta}=\sqrt{1348}=\sqrt{4*337}=\sqrt{4}*\sqrt{337}=2\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{337}}{2*-28}=\frac{-26-2\sqrt{337}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{337}}{2*-28}=\frac{-26+2\sqrt{337}}{-56}
$