X(x+10)=274

Solution for X(x+10)=274 equation:

X(X+10)=274

We move all terms to the left:

X(X+10)-(274)=0

We multiply parentheses

X^2+10X-274=0

a = 1; b = 10; c = -274;
Δ = b2-4ac
Δ = 102-4·1·(-274)
Δ = 1196
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:

$\sqrt{\Delta}=\sqrt{1196}=\sqrt{4*299}=\sqrt{4}*\sqrt{299}=2\sqrt{299}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{299}}{2*1}=\frac{-10-2\sqrt{299}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{299}}{2*1}=\frac{-10+2\sqrt{299}}{2}
$