x=2x^2-28x-7

Solution for x=2x^2-28x-7 equation:

x=2x^2-28x-7

We move all terms to the left:

x-(2x^2-28x-7)=0

We get rid of parentheses

-2x^2+x+28x+7=0

We add all the numbers together, and all the variables

-2x^2+29x+7=0

a = -2; b = 29; c = +7;
Δ = b2-4ac
Δ = 292-4·(-2)·7
Δ = 897
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-\sqrt{897}}{2*-2}=\frac{-29-\sqrt{897}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{897}}{2*-2}=\frac{-29+\sqrt{897}}{-4}
$