((-4x^2)+7x+8)-((-5x^2)-x-7)=8

Solution for ((-4x^2)+7x+8)-((-5x^2)-x-7)=8 equation:

((-4x^2)+7x+8)-((-5x^2)-x-7)=8

We move all terms to the left:

((-4x^2)+7x+8)-((-5x^2)-x-7)-(8)=0


We calculate terms in parentheses: +((-4x^2)+7x+8), so:

(-4x^2)+7x+8

We get rid of parentheses

-4x^2+7x+8

Back to the equation:

+(-4x^2+7x+8)



We calculate terms in parentheses: -((-5x^2)-x-7), so:

(-5x^2)-x-7

We add all the numbers together, and all the variables

(-5x^2)-1x-7

We get rid of parentheses

-5x^2-1x-7

Back to the equation:

-(-5x^2-1x-7)


We get rid of parentheses

-4x^2+5x^2+7x+1x+8+7-8=0

We add all the numbers together, and all the variables

x^2+8x+7=0

a = 1; b = 8; c = +7;
Δ = b2-4ac
Δ = 82-4·1·7
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6}{2*1}=\frac{-2}{2}
=-1
$