3x=5(-9/14)+5

Solution for 3x=5(-9/14)+5 equation:

3x=5(-9/14)+5

We move all terms to the left:

3x-(5(-9/14)+5)=0

We multiply all the terms by the denominator


3x*14)+5)-(5(-9=0

Wy multiply elements

42x^2-9=0

a = 42; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·42·(-9)
Δ = 1512
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:

$\sqrt{\Delta}=\sqrt{1512}=\sqrt{36*42}=\sqrt{36}*\sqrt{42}=6\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{42}}{2*42}=\frac{0-6\sqrt{42}}{84}
=-\frac{6\sqrt{42}}{84}
=-\frac{\sqrt{42}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{42}}{2*42}=\frac{0+6\sqrt{42}}{84}
=\frac{6\sqrt{42}}{84}
=\frac{\sqrt{42}}{14}
$