X2+7x-24=10x+16

Solution for X2+7x-24=10x+16 equation:

X2+7X-24=10X+16

We move all terms to the left:

X2+7X-24-(10X+16)=0

We add all the numbers together, and all the variables

X^2+7X-(10X+16)-24=0

We get rid of parentheses

X^2+7X-10X-16-24=0

We add all the numbers together, and all the variables

X^2-3X-40=0

a = 1; b = -3; c = -40;
Δ = b2-4ac
Δ = -32-4·1·(-40)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-13}{2*1}=\frac{-10}{2}
=-5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+13}{2*1}=\frac{16}{2}
=8
$