5x2-55x=140

Solution for 5x2-55x=140 equation:

5x^2-55x=140

We move all terms to the left:

5x^2-55x-(140)=0

a = 5; b = -55; c = -140;
Δ = b2-4ac
Δ = -552-4·5·(-140)
Δ = 5825
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:

$\sqrt{\Delta}=\sqrt{5825}=\sqrt{25*233}=\sqrt{25}*\sqrt{233}=5\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5\sqrt{233}}{2*5}=\frac{55-5\sqrt{233}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5\sqrt{233}}{2*5}=\frac{55+5\sqrt{233}}{10}
$