(2x^2+11x+8)/(2x+5)=0

Solution for (2x^2+11x+8)/(2x+5)=0 equation:

(2x^2+11x+8)/(2x+5)=0


Domain of the equation: (2x+5)!=0

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

2x!=-5

x!=-5/2

x!=-2+1/2

x∈R


We multiply all the terms by the denominator


(2x^2+11x+8)=0

We get rid of parentheses

2x^2+11x+8=0

a = 2; b = 11; c = +8;
Δ = b2-4ac
Δ = 112-4·2·8
Δ = 57
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{-(11)-\sqrt{57}}{2*2}=\frac{-11-\sqrt{57}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{57}}{2*2}=\frac{-11+\sqrt{57}}{4}
$