2x^2-14x=32

Solution for 2x^2-14x=32 equation:

2x^2-14x=32

We move all terms to the left:

2x^2-14x-(32)=0

a = 2; b = -14; c = -32;
Δ = b2-4ac
Δ = -142-4·2·(-32)
Δ = 452
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:

$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{113}}{2*2}=\frac{14-2\sqrt{113}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{113}}{2*2}=\frac{14+2\sqrt{113}}{4}
$