5x^2-18=-4x^2-7x-2

Solution for 5x^2-18=-4x^2-7x-2 equation:

5x^2-18=-4x^2-7x-2

We move all terms to the left:

5x^2-18-(-4x^2-7x-2)=0

We get rid of parentheses

5x^2+4x^2+7x+2-18=0

We add all the numbers together, and all the variables

9x^2+7x-16=0

a = 9; b = 7; c = -16;
Δ = b2-4ac
Δ = 72-4·9·(-16)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-25}{2*9}=\frac{-32}{18}
=-1+7/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+25}{2*9}=\frac{18}{18}
=1
$