(-1/3)(9x+42)-5x=-70

Solution for (-1/3)(9x+42)-5x=-70 equation:

(-1/3)(9x+42)-5x=-70

We move all terms to the left:

(-1/3)(9x+42)-5x-(-70)=0


Domain of the equation: 3)(9x+42)!=0

x∈R


We add all the numbers together, and all the variables

-5x+(-1/3)(9x+42)+70=0

We multiply parentheses ..

(-9x^2-1/3*42)-5x+70=0

We multiply all the terms by the denominator


(-9x^2-1-5x*3*42)+70*3*42)=0

We add all the numbers together, and all the variables

(-9x^2-1-5x*3*42)=0

We get rid of parentheses

-9x^2-5x*3*42-1=0

Wy multiply elements

-9x^2-630x*4-1=0

Wy multiply elements

-9x^2-2520x-1=0

a = -9; b = -2520; c = -1;
Δ = b2-4ac
Δ = -25202-4·(-9)·(-1)
Δ = 6350364
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:

$\sqrt{\Delta}=\sqrt{6350364}=\sqrt{36*176399}=\sqrt{36}*\sqrt{176399}=6\sqrt{176399}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2520)-6\sqrt{176399}}{2*-9}=\frac{2520-6\sqrt{176399}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2520)+6\sqrt{176399}}{2*-9}=\frac{2520+6\sqrt{176399}}{-18}
$