2/5x+6=4x-3

Solution for 2/5x+6=4x-3 equation:

2/5x+6=4x-3

We move all terms to the left:

2/5x+6-(4x-3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-4x+3+6=0

We multiply all the terms by the denominator


-4x*5x+3*5x+6*5x+2=0

Wy multiply elements

-20x^2+15x+30x+2=0

We add all the numbers together, and all the variables

-20x^2+45x+2=0

a = -20; b = 45; c = +2;
Δ = b2-4ac
Δ = 452-4·(-20)·2
Δ = 2185
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{-(45)-\sqrt{2185}}{2*-20}=\frac{-45-\sqrt{2185}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2185}}{2*-20}=\frac{-45+\sqrt{2185}}{-40}
$