22x+7x^2=24

Solution for 22x+7x^2=24 equation:

22x+7x^2=24

We move all terms to the left:

22x+7x^2-(24)=0

a = 7; b = 22; c = -24;
Δ = b2-4ac
Δ = 222-4·7·(-24)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-34}{2*7}=\frac{-56}{14}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+34}{2*7}=\frac{12}{14}
=6/7
$