5x^2+7x+8=4x^2-10x-2

Solution for 5x^2+7x+8=4x^2-10x-2 equation:

5x^2+7x+8=4x^2-10x-2

We move all terms to the left:

5x^2+7x+8-(4x^2-10x-2)=0

We get rid of parentheses

5x^2-4x^2+7x+10x+2+8=0

We add all the numbers together, and all the variables

x^2+17x+10=0

a = 1; b = 17; c = +10;
Δ = b2-4ac
Δ = 172-4·1·10
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{249}}{2*1}=\frac{-17-\sqrt{249}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{249}}{2*1}=\frac{-17+\sqrt{249}}{2}
$