X^2-3x+10x+7=12x+21

Solution for X^2-3x+10x+7=12x+21 equation:

X^2-3X+10X+7=12X+21

We move all terms to the left:

X^2-3X+10X+7-(12X+21)=0

We add all the numbers together, and all the variables

X^2+7X-(12X+21)+7=0

We get rid of parentheses

X^2+7X-12X-21+7=0

We add all the numbers together, and all the variables

X^2-5X-14=0

a = 1; b = -5; c = -14;
Δ = b2-4ac
Δ = -52-4·1·(-14)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-9}{2*1}=\frac{-4}{2}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+9}{2*1}=\frac{14}{2}
=7
$