14-(6x-5)=5(2x-1)4x

Solution for 14-(6x-5)=5(2x-1)4x equation:

14-(6x-5)=5(2x-1)4x

We move all terms to the left:

14-(6x-5)-(5(2x-1)4x)=0

We get rid of parentheses

-6x-(5(2x-1)4x)+5+14=0


We calculate terms in parentheses: -(5(2x-1)4x), so:

5(2x-1)4x

We multiply parentheses

40x^2-20x

Back to the equation:

-(40x^2-20x)


We add all the numbers together, and all the variables

-6x-(40x^2-20x)+19=0

We get rid of parentheses

-40x^2-6x+20x+19=0

We add all the numbers together, and all the variables

-40x^2+14x+19=0

a = -40; b = 14; c = +19;
Δ = b2-4ac
Δ = 142-4·(-40)·19
Δ = 3236
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:

$\sqrt{\Delta}=\sqrt{3236}=\sqrt{4*809}=\sqrt{4}*\sqrt{809}=2\sqrt{809}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{809}}{2*-40}=\frac{-14-2\sqrt{809}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{809}}{2*-40}=\frac{-14+2\sqrt{809}}{-80}
$