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

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

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

We move all terms to the left:

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


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+1x+7x+7+8=0

We add all the numbers together, and all the variables

x^2+8x+15=0

a = 1; b = 8; c = +15;
Δ = b2-4ac
Δ = 82-4·1·15
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2}{2*1}=\frac{-6}{2}
=-3
$