5x+7=-14/8x

Solution for 5x+7=-14/8x equation:

5x+7=-14/8x

We move all terms to the left:

5x+7-(-14/8x)=0


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

5x+14/8x+7=0

We multiply all the terms by the denominator


5x*8x+7*8x+14=0

Wy multiply elements

40x^2+56x+14=0

a = 40; b = 56; c = +14;
Δ = b2-4ac
Δ = 562-4·40·14
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-8\sqrt{14}}{2*40}=\frac{-56-8\sqrt{14}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+8\sqrt{14}}{2*40}=\frac{-56+8\sqrt{14}}{80}
$