3x=-(5(7-4x)+6)/5

Solution for 3x=-(5(7-4x)+6)/5 equation:

3x=-(5(7-4x)+6)/5

We move all terms to the left:

3x-(-(5(7-4x)+6)/5)=0

We add all the numbers together, and all the variables

3x-(-(5(-4x+7)+6)/5)=0

We multiply all the terms by the denominator


3x*5)-(-(5(-4x+7)+6)=0


We calculate terms in parentheses: -(5(-4x+7)+6), so:

5(-4x+7)+6

We multiply parentheses

-20x+35+6

We add all the numbers together, and all the variables

-20x+41

Back to the equation:

-(-20x+41)


Wy multiply elements

15x^2-(-20x+41)=0

We get rid of parentheses

15x^2+20x-41=0

a = 15; b = 20; c = -41;
Δ = b2-4ac
Δ = 202-4·15·(-41)
Δ = 2860
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:

$\sqrt{\Delta}=\sqrt{2860}=\sqrt{4*715}=\sqrt{4}*\sqrt{715}=2\sqrt{715}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{715}}{2*15}=\frac{-20-2\sqrt{715}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{715}}{2*15}=\frac{-20+2\sqrt{715}}{30}
$