X.3(2x-5)=2(3x-2)

Solution for X.3(2x-5)=2(3x-2) equation:

X.3(2X-5)=2(3X-2)

We move all terms to the left:

X.3(2X-5)-(2(3X-2))=0

We multiply parentheses

2X^2-5X-(2(3X-2))=0


We calculate terms in parentheses: -(2(3X-2)), so:

2(3X-2)

We multiply parentheses

6X-4

Back to the equation:

-(6X-4)


We get rid of parentheses

2X^2-5X-6X+4=0

We add all the numbers together, and all the variables

2X^2-11X+4=0

a = 2; b = -11; c = +4;
Δ = b2-4ac
Δ = -112-4·2·4
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{89}}{2*2}=\frac{11-\sqrt{89}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{89}}{2*2}=\frac{11+\sqrt{89}}{4}
$