0=7x2+16x-5

Solution for 0=7x2+16x-5 equation:

0=7x^2+16x-5

We move all terms to the left:

0-(7x^2+16x-5)=0

We add all the numbers together, and all the variables

-(7x^2+16x-5)=0

We get rid of parentheses

-7x^2-16x+5=0

a = -7; b = -16; c = +5;
Δ = b2-4ac
Δ = -162-4·(-7)·5
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-6\sqrt{11}}{2*-7}=\frac{16-6\sqrt{11}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+6\sqrt{11}}{2*-7}=\frac{16+6\sqrt{11}}{-14}
$