10x^2+10x=186

Solution for 10x^2+10x=186 equation:

10x^2+10x=186

We move all terms to the left:

10x^2+10x-(186)=0

a = 10; b = 10; c = -186;
Δ = b2-4ac
Δ = 102-4·10·(-186)
Δ = 7540
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:

$\sqrt{\Delta}=\sqrt{7540}=\sqrt{4*1885}=\sqrt{4}*\sqrt{1885}=2\sqrt{1885}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{1885}}{2*10}=\frac{-10-2\sqrt{1885}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{1885}}{2*10}=\frac{-10+2\sqrt{1885}}{20}
$