-14+5x=32x(x-28)+18

Solution for -14+5x=32x(x-28)+18 equation:

-14+5x=32x(x-28)+18

We move all terms to the left:

-14+5x-(32x(x-28)+18)=0


We calculate terms in parentheses: -(32x(x-28)+18), so:

32x(x-28)+18

We multiply parentheses

32x^2-896x+18

Back to the equation:

-(32x^2-896x+18)


We get rid of parentheses

-32x^2+5x+896x-18-14=0

We add all the numbers together, and all the variables

-32x^2+901x-32=0

a = -32; b = 901; c = -32;
Δ = b2-4ac
Δ = 9012-4·(-32)·(-32)
Δ = 807705
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:

$\sqrt{\Delta}=\sqrt{807705}=\sqrt{9*89745}=\sqrt{9}*\sqrt{89745}=3\sqrt{89745}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(901)-3\sqrt{89745}}{2*-32}=\frac{-901-3\sqrt{89745}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(901)+3\sqrt{89745}}{2*-32}=\frac{-901+3\sqrt{89745}}{-64}
$