x^2-22x^2+x+114=0

Solution for x^2-22x^2+x+114=0 equation:

x^2-22x^2+x+114=0

We add all the numbers together, and all the variables

-21x^2+x+114=0

a = -21; b = 1; c = +114;
Δ = b2-4ac
Δ = 12-4·(-21)·114
Δ = 9577
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{-(1)-\sqrt{9577}}{2*-21}=\frac{-1-\sqrt{9577}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{9577}}{2*-21}=\frac{-1+\sqrt{9577}}{-42}
$