5x^2+7=16x+4

Solution for 5x^2+7=16x+4 equation:

5x^2+7=16x+4

We move all terms to the left:

5x^2+7-(16x+4)=0

We get rid of parentheses

5x^2-16x-4+7=0

We add all the numbers together, and all the variables

5x^2-16x+3=0

a = 5; b = -16; c = +3;
Δ = b2-4ac
Δ = -162-4·5·3
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-14}{2*5}=\frac{2}{10}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+14}{2*5}=\frac{30}{10}
=3
$