-2x2+146=-34

Solution for -2x2+146=-34 equation:

-2x^2+146=-34

We move all terms to the left:

-2x^2+146-(-34)=0

We add all the numbers together, and all the variables

-2x^2+180=0

a = -2; b = 0; c = +180;
Δ = b2-4ac
Δ = 02-4·(-2)·180
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{10}}{2*-2}=\frac{0-12\sqrt{10}}{-4}
=-\frac{12\sqrt{10}}{-4}
=-\frac{3\sqrt{10}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{10}}{2*-2}=\frac{0+12\sqrt{10}}{-4}
=\frac{12\sqrt{10}}{-4}
=\frac{3\sqrt{10}}{-1}
$