Y=2x+3/4x-5

Solution for Y=2x+3/4x-5 equation:

=2Y+3/4Y-5

We move all terms to the left:

-(2Y+3/4Y-5)=0


Domain of the equation: 4Y-5)!=0

Y∈R


We get rid of parentheses

-2Y-3/4Y+5=0

We multiply all the terms by the denominator


-2Y*4Y+5*4Y-3=0

Wy multiply elements

-8Y^2+20Y-3=0

a = -8; b = 20; c = -3;
Δ = b2-4ac
Δ = 202-4·(-8)·(-3)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{19}}{2*-8}=\frac{-20-4\sqrt{19}}{-16}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{19}}{2*-8}=\frac{-20+4\sqrt{19}}{-16}
$