10x^2-30x=50

Solution for 10x^2-30x=50 equation:

10x^2-30x=50

We move all terms to the left:

10x^2-30x-(50)=0

a = 10; b = -30; c = -50;
Δ = b2-4ac
Δ = -302-4·10·(-50)
Δ = 2900
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:

$\sqrt{\Delta}=\sqrt{2900}=\sqrt{100*29}=\sqrt{100}*\sqrt{29}=10\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{29}}{2*10}=\frac{30-10\sqrt{29}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{29}}{2*10}=\frac{30+10\sqrt{29}}{20}
$