X(3x+20)=1463

Solution for X(3x+20)=1463 equation:

X(3X+20)=1463

We move all terms to the left:

X(3X+20)-(1463)=0

We multiply parentheses

3X^2+20X-1463=0

a = 3; b = 20; c = -1463;
Δ = b2-4ac
Δ = 202-4·3·(-1463)
Δ = 17956
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17956}=134$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-134}{2*3}=\frac{-154}{6}
=-25+2/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+134}{2*3}=\frac{114}{6}
=19
$