Y=4x-7/2X+3

Solution for Y=4x-7/2X+3 equation:

=4Y-7/2Y+3

We move all terms to the left:

-(4Y-7/2Y+3)=0


Domain of the equation: 2Y+3)!=0

Y∈R


We get rid of parentheses

-4Y+7/2Y-3=0

We multiply all the terms by the denominator


-4Y*2Y-3*2Y+7=0

Wy multiply elements

-8Y^2-6Y+7=0

a = -8; b = -6; c = +7;
Δ = b2-4ac
Δ = -62-4·(-8)·7
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{65}}{2*-8}=\frac{6-2\sqrt{65}}{-16}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{65}}{2*-8}=\frac{6+2\sqrt{65}}{-16}
$