7x2+x=49

Solution for 7x2+x=49 equation:

7x^2+x=49

We move all terms to the left:

7x^2+x-(49)=0

a = 7; b = 1; c = -49;
Δ = b2-4ac
Δ = 12-4·7·(-49)
Δ = 1373
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{1373}}{2*7}=\frac{-1-\sqrt{1373}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1373}}{2*7}=\frac{-1+\sqrt{1373}}{14}
$