2n^2*7=-4n+5

Solution for 2n^2*7=-4n+5 equation:

2n^2*7=-4n+5

We move all terms to the left:

2n^2*7-(-4n+5)=0

Wy multiply elements

14n^2-(-4n+5)=0

We get rid of parentheses

14n^2+4n-5=0

a = 14; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·14·(-5)
Δ = 296
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:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{74}}{2*14}=\frac{-4-2\sqrt{74}}{28}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{74}}{2*14}=\frac{-4+2\sqrt{74}}{28}
$