2n2=-10n-7

Solution for 2n2=-10n-7 equation:

2n^2=-10n-7

We move all terms to the left:

2n^2-(-10n-7)=0

We get rid of parentheses

2n^2+10n+7=0

a = 2; b = 10; c = +7;
Δ = b2-4ac
Δ = 102-4·2·7
Δ = 44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{11}}{2*2}=\frac{-10-2\sqrt{11}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{11}}{2*2}=\frac{-10+2\sqrt{11}}{4}
$