2x^2=77x+5

Solution for 2x^2=77x+5 equation:

2x^2=77x+5

We move all terms to the left:

2x^2-(77x+5)=0

We get rid of parentheses

2x^2-77x-5=0

a = 2; b = -77; c = -5;
Δ = b2-4ac
Δ = -772-4·2·(-5)
Δ = 5969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-\sqrt{5969}}{2*2}=\frac{77-\sqrt{5969}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+\sqrt{5969}}{2*2}=\frac{77+\sqrt{5969}}{4}
$