3/7(x)=7x+8

Solution for 3/7(x)=7x+8 equation:

3/7(x)=7x+8

We move all terms to the left:

3/7(x)-(7x+8)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

3/7x-7x-8=0

We multiply all the terms by the denominator


-7x*7x-8*7x+3=0

Wy multiply elements

-49x^2-56x+3=0

a = -49; b = -56; c = +3;
Δ = b2-4ac
Δ = -562-4·(-49)·3
Δ = 3724
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:

$\sqrt{\Delta}=\sqrt{3724}=\sqrt{196*19}=\sqrt{196}*\sqrt{19}=14\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-14\sqrt{19}}{2*-49}=\frac{56-14\sqrt{19}}{-98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+14\sqrt{19}}{2*-49}=\frac{56+14\sqrt{19}}{-98}
$