18=7x+25x^2

Solution for 18=7x+25x^2 equation:

18=7x+25x^2

We move all terms to the left:

18-(7x+25x^2)=0

We get rid of parentheses

-25x^2-7x+18=0

a = -25; b = -7; c = +18;
Δ = b2-4ac
Δ = -72-4·(-25)·18
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-43}{2*-25}=\frac{-36}{-50}
=18/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+43}{2*-25}=\frac{50}{-50}
=-1
$