7x+2x^2=2272

Solution for 7x+2x^2=2272 equation:

7x+2x^2=2272

We move all terms to the left:

7x+2x^2-(2272)=0

a = 2; b = 7; c = -2272;
Δ = b2-4ac
Δ = 72-4·2·(-2272)
Δ = 18225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18225}=135$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-135}{2*2}=\frac{-142}{4}
=-35+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+135}{2*2}=\frac{128}{4}
=32
$