Y=4x+3/7x-8

Solution for Y=4x+3/7x-8 equation:

=4Y+3/7Y-8

We move all terms to the left:

-(4Y+3/7Y-8)=0


Domain of the equation: 7Y-8)!=0

Y∈R


We get rid of parentheses

-4Y-3/7Y+8=0

We multiply all the terms by the denominator


-4Y*7Y+8*7Y-3=0

Wy multiply elements

-28Y^2+56Y-3=0

a = -28; b = 56; c = -3;
Δ = b2-4ac
Δ = 562-4·(-28)·(-3)
Δ = 2800
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:

$\sqrt{\Delta}=\sqrt{2800}=\sqrt{400*7}=\sqrt{400}*\sqrt{7}=20\sqrt{7}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-20\sqrt{7}}{2*-28}=\frac{-56-20\sqrt{7}}{-56}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+20\sqrt{7}}{2*-28}=\frac{-56+20\sqrt{7}}{-56}
$