2x^2+x=7.7

Solution for 2x^2+x=7.7 equation:

2x^2+x=7.7

We move all terms to the left:

2x^2+x-(7.7)=0

We add all the numbers together, and all the variables

2x^2+x-7.7=0

a = 2; b = 1; c = -7.7;
Δ = b2-4ac
Δ = 12-4·2·(-7.7)
Δ = 62.6
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{-(1)-\sqrt{62.6}}{2*2}=\frac{-1-\sqrt{62.6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{62.6}}{2*2}=\frac{-1+\sqrt{62.6}}{4}
$