5x^2-43x-125=7x

Solution for 5x^2-43x-125=7x equation:

5x^2-43x-125=7x

We move all terms to the left:

5x^2-43x-125-(7x)=0

We add all the numbers together, and all the variables

5x^2-50x-125=0

a = 5; b = -50; c = -125;
Δ = b2-4ac
Δ = -502-4·5·(-125)
Δ = 5000
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:

$\sqrt{\Delta}=\sqrt{5000}=\sqrt{2500*2}=\sqrt{2500}*\sqrt{2}=50\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50\sqrt{2}}{2*5}=\frac{50-50\sqrt{2}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50\sqrt{2}}{2*5}=\frac{50+50\sqrt{2}}{10}
$