X^2+10x-74=13

Solution for X^2+10x-74=13 equation:

X^2+10X-74=13

We move all terms to the left:

X^2+10X-74-(13)=0

We add all the numbers together, and all the variables

X^2+10X-87=0

a = 1; b = 10; c = -87;
Δ = b2-4ac
Δ = 102-4·1·(-87)
Δ = 448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-8\sqrt{7}}{2*1}=\frac{-10-8\sqrt{7}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+8\sqrt{7}}{2*1}=\frac{-10+8\sqrt{7}}{2}
$