4x^2+9x-14=x

Solution for 4x^2+9x-14=x equation:

4x^2+9x-14=x

We move all terms to the left:

4x^2+9x-14-(x)=0

We add all the numbers together, and all the variables

4x^2+8x-14=0

a = 4; b = 8; c = -14;
Δ = b2-4ac
Δ = 82-4·4·(-14)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12\sqrt{2}}{2*4}=\frac{-8-12\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12\sqrt{2}}{2*4}=\frac{-8+12\sqrt{2}}{8}
$