8/5x+3=6x+5

Solution for 8/5x+3=6x+5 equation:

8/5x+3=6x+5

We move all terms to the left:

8/5x+3-(6x+5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

8/5x-6x-5+3=0

We multiply all the terms by the denominator


-6x*5x-5*5x+3*5x+8=0

Wy multiply elements

-30x^2-25x+15x+8=0

We add all the numbers together, and all the variables

-30x^2-10x+8=0

a = -30; b = -10; c = +8;
Δ = b2-4ac
Δ = -102-4·(-30)·8
Δ = 1060
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:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{265}}{2*-30}=\frac{10-2\sqrt{265}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{265}}{2*-30}=\frac{10+2\sqrt{265}}{-60}
$