3x+10=7x2+2

Solution for 3x+10=7x2+2 equation:

3x+10=7x^2+2

We move all terms to the left:

3x+10-(7x^2+2)=0

We get rid of parentheses

-7x^2+3x-2+10=0

We add all the numbers together, and all the variables

-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}
$