2x^2+5x=77

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

2x^2+5x=77

We move all terms to the left:

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

a = 2; b = 5; c = -77;
Δ = b2-4ac
Δ = 52-4·2·(-77)
Δ = 641
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{-(5)-\sqrt{641}}{2*2}=\frac{-5-\sqrt{641}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{641}}{2*2}=\frac{-5+\sqrt{641}}{4}
$