15+26x=4x(8x-2)+19

Solution for 15+26x=4x(8x-2)+19 equation:

15+26x=4x(8x-2)+19

We move all terms to the left:

15+26x-(4x(8x-2)+19)=0


We calculate terms in parentheses: -(4x(8x-2)+19), so:

4x(8x-2)+19

We multiply parentheses

32x^2-8x+19

Back to the equation:

-(32x^2-8x+19)


We get rid of parentheses

-32x^2+26x+8x-19+15=0

We add all the numbers together, and all the variables

-32x^2+34x-4=0

a = -32; b = 34; c = -4;
Δ = b2-4ac
Δ = 342-4·(-32)·(-4)
Δ = 644
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:

$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{161}}{2*-32}=\frac{-34-2\sqrt{161}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{161}}{2*-32}=\frac{-34+2\sqrt{161}}{-64}
$