X^2-3x/4=5x-15/4

Solution for X^2-3x/4=5x-15/4 equation:

X^2-3X/4=5X-15/4

We move all terms to the left:

X^2-3X/4-(5X-15/4)=0

We add all the numbers together, and all the variables

X^2-3X/4-(+5X-15/4)=0

We get rid of parentheses

X^2-3X/4-5X+15/4=0

We multiply all the terms by the denominator


X^2*4-3X-5X*4+15=0

Wy multiply elements

4X^2-3X-20X+15=0

We add all the numbers together, and all the variables

4X^2-23X+15=0

a = 4; b = -23; c = +15;
Δ = b2-4ac
Δ = -232-4·4·15
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-17}{2*4}=\frac{6}{8}
=3/4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+17}{2*4}=\frac{40}{8}
=5
$