x^2+7x+10=100

Solution for x^2+7x+10=100 equation:

x^2+7x+10=100

We move all terms to the left:

x^2+7x+10-(100)=0

We add all the numbers together, and all the variables

x^2+7x-90=0

a = 1; b = 7; c = -90;
Δ = b2-4ac
Δ = 72-4·1·(-90)
Δ = 409
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{-(7)-\sqrt{409}}{2*1}=\frac{-7-\sqrt{409}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{409}}{2*1}=\frac{-7+\sqrt{409}}{2}
$