3x=(-2/5)(4x-10)

Solution for 3x=(-2/5)(4x-10) equation:

3x=(-2/5)(4x-10)

We move all terms to the left:

3x-((-2/5)(4x-10))=0


Domain of the equation: 5)(4x-10))!=0

x∈R


We multiply parentheses ..

-((-8x^2-2/5*-10))+3x=0

We multiply all the terms by the denominator


-((-8x^2-2+3x*5*-10))=0


We calculate terms in parentheses: -((-8x^2-2+3x*5*-10)), so:

(-8x^2-2+3x*5*-10)

We get rid of parentheses

-8x^2+3x*5*-2-10

We add all the numbers together, and all the variables

-8x^2+3x*5*-12

Wy multiply elements

-8x^2+15x^2-12

We add all the numbers together, and all the variables

7x^2-12

Back to the equation:

-(7x^2-12)


We get rid of parentheses

-7x^2+12=0

a = -7; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-7)·12
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{21}}{2*-7}=\frac{0-4\sqrt{21}}{-14}
=-\frac{4\sqrt{21}}{-14}
=-\frac{2\sqrt{21}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{21}}{2*-7}=\frac{0+4\sqrt{21}}{-14}
=\frac{4\sqrt{21}}{-14}
=\frac{2\sqrt{21}}{-7}
$