7-3x=8x2

Solution for 7-3x=8x2 equation:

7-3x=8x^2

We move all terms to the left:

7-3x-(8x^2)=0

determiningTheFunctionDomain
-8x^2-3x+7=0

a = -8; b = -3; c = +7;
Δ = b2-4ac
Δ = -32-4·(-8)·7
Δ = 233
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{-(-3)-\sqrt{233}}{2*-8}=\frac{3-\sqrt{233}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{233}}{2*-8}=\frac{3+\sqrt{233}}{-16}
$