6y=-3+4(-9/13)

Solution for 6y=-3+4(-9/13) equation:

6y=-3+4(-9/13)

We move all terms to the left:

6y-(-3+4(-9/13))=0

We multiply all the terms by the denominator


6y*13))-(-3+4(-9=0

Wy multiply elements

78y^2-9=0

a = 78; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·78·(-9)
Δ = 2808
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2808}=\sqrt{36*78}=\sqrt{36}*\sqrt{78}=6\sqrt{78}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{78}}{2*78}=\frac{0-6\sqrt{78}}{156}
=-\frac{6\sqrt{78}}{156}
=-\frac{\sqrt{78}}{26}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{78}}{2*78}=\frac{0+6\sqrt{78}}{156}
=\frac{6\sqrt{78}}{156}
=\frac{\sqrt{78}}{26}
$