48=8x^2-7x

Solution for 48=8x^2-7x equation:

48=8x^2-7x

We move all terms to the left:

48-(8x^2-7x)=0

We get rid of parentheses

-8x^2+7x+48=0

a = -8; b = 7; c = +48;
Δ = b2-4ac
Δ = 72-4·(-8)·48
Δ = 1585
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{1585}}{2*-8}=\frac{-7-\sqrt{1585}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{1585}}{2*-8}=\frac{-7+\sqrt{1585}}{-16}
$