7x+3x^2=1340

Solution for 7x+3x^2=1340 equation:

7x+3x^2=1340

We move all terms to the left:

7x+3x^2-(1340)=0

a = 3; b = 7; c = -1340;
Δ = b2-4ac
Δ = 72-4·3·(-1340)
Δ = 16129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16129}=127$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-127}{2*3}=\frac{-134}{6}
=-22+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+127}{2*3}=\frac{120}{6}
=20
$