5x^2+7=16x

Solution for 5x^2+7=16x equation:

5x^2+7=16x

We move all terms to the left:

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

a = 5; b = -16; c = +7;
Δ = b2-4ac
Δ = -162-4·5·7
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{29}}{2*5}=\frac{16-2\sqrt{29}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{29}}{2*5}=\frac{16+2\sqrt{29}}{10}
$