X(2x-13)=3x-30

Solution for X(2x-13)=3x-30 equation:

X(2X-13)=3X-30

We move all terms to the left:

X(2X-13)-(3X-30)=0

We multiply parentheses

2X^2-13X-(3X-30)=0

We get rid of parentheses

2X^2-13X-3X+30=0

We add all the numbers together, and all the variables

2X^2-16X+30=0

a = 2; b = -16; c = +30;
Δ = b2-4ac
Δ = -162-4·2·30
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4}{2*2}=\frac{12}{4}
=3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4}{2*2}=\frac{20}{4}
=5
$