8=7x^2+3x

Solution for 8=7x^2+3x equation:

8=7x^2+3x

We move all terms to the left:

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

We get rid of parentheses

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

a = -7; b = -3; c = +8;
Δ = b2-4ac
Δ = -32-4·(-7)·8
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*-7}=\frac{3-\sqrt{233}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{233}}{2*-7}=\frac{3+\sqrt{233}}{-14}
$