10a^2-20a-50=7

Solution for 10a^2-20a-50=7 equation:

10a^2-20a-50=7

We move all terms to the left:

10a^2-20a-50-(7)=0

We add all the numbers together, and all the variables

10a^2-20a-57=0

a = 10; b = -20; c = -57;
Δ = b2-4ac
Δ = -202-4·10·(-57)
Δ = 2680
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2680}=\sqrt{4*670}=\sqrt{4}*\sqrt{670}=2\sqrt{670}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{670}}{2*10}=\frac{20-2\sqrt{670}}{20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{670}}{2*10}=\frac{20+2\sqrt{670}}{20}
$