8(3x-2)14x=2(4x-7)+15

Solution for 8(3x-2)14x=2(4x-7)+15 equation:

8(3x-2)14x=2(4x-7)+15

We move all terms to the left:

8(3x-2)14x-(2(4x-7)+15)=0

We multiply parentheses

336x^2-224x-(2(4x-7)+15)=0


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

2(4x-7)+15

We multiply parentheses

8x-14+15

We add all the numbers together, and all the variables

8x+1

Back to the equation:

-(8x+1)


We get rid of parentheses

336x^2-224x-8x-1=0

We add all the numbers together, and all the variables

336x^2-232x-1=0

a = 336; b = -232; c = -1;
Δ = b2-4ac
Δ = -2322-4·336·(-1)
Δ = 55168
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:

$\sqrt{\Delta}=\sqrt{55168}=\sqrt{64*862}=\sqrt{64}*\sqrt{862}=8\sqrt{862}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-232)-8\sqrt{862}}{2*336}=\frac{232-8\sqrt{862}}{672}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-232)+8\sqrt{862}}{2*336}=\frac{232+8\sqrt{862}}{672}
$