8x^2-57x=-7

Solution for 8x^2-57x=-7 equation:

8x^2-57x=-7

We move all terms to the left:

8x^2-57x-(-7)=0

We add all the numbers together, and all the variables

8x^2-57x+7=0

a = 8; b = -57; c = +7;
Δ = b2-4ac
Δ = -572-4·8·7
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-55}{2*8}=\frac{2}{16}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+55}{2*8}=\frac{112}{16}
=7
$