5x+7x^2=700

Solution for 5x+7x^2=700 equation:

5x+7x^2=700

We move all terms to the left:

5x+7x^2-(700)=0

a = 7; b = 5; c = -700;
Δ = b2-4ac
Δ = 52-4·7·(-700)
Δ = 19625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{19625}=\sqrt{25*785}=\sqrt{25}*\sqrt{785}=5\sqrt{785}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{785}}{2*7}=\frac{-5-5\sqrt{785}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{785}}{2*7}=\frac{-5+5\sqrt{785}}{14}
$