14x-5x^2=-7

Solution for 14x-5x^2=-7 equation:

14x-5x^2=-7

We move all terms to the left:

14x-5x^2-(-7)=0

We add all the numbers together, and all the variables

-5x^2+14x+7=0

a = -5; b = 14; c = +7;
Δ = b2-4ac
Δ = 142-4·(-5)·7
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{21}}{2*-5}=\frac{-14-4\sqrt{21}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{21}}{2*-5}=\frac{-14+4\sqrt{21}}{-10}
$