(10x^2+74x-5)/(x+8)=0

Solution for (10x^2+74x-5)/(x+8)=0 equation:

(10x^2+74x-5)/(x+8)=0


Domain of the equation: (x+8)!=0

We move all terms containing x to the left, all other terms to the right

x!=-8

x∈R


We multiply all the terms by the denominator


(10x^2+74x-5)=0

We get rid of parentheses

10x^2+74x-5=0

a = 10; b = 74; c = -5;
Δ = b2-4ac
Δ = 742-4·10·(-5)
Δ = 5676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5676}=\sqrt{4*1419}=\sqrt{4}*\sqrt{1419}=2\sqrt{1419}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(74)-2\sqrt{1419}}{2*10}=\frac{-74-2\sqrt{1419}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74)+2\sqrt{1419}}{2*10}=\frac{-74+2\sqrt{1419}}{20}
$