x^2+102x+341=-6x^2+5+4x

Solution for x^2+102x+341=-6x^2+5+4x equation:

x^2+102x+341=-6x^2+5+4x

We move all terms to the left:

x^2+102x+341-(-6x^2+5+4x)=0

We get rid of parentheses

x^2+6x^2-4x+102x-5+341=0

We add all the numbers together, and all the variables

7x^2+98x+336=0

a = 7; b = 98; c = +336;
Δ = b2-4ac
Δ = 982-4·7·336
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(98)-14}{2*7}=\frac{-112}{14}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(98)+14}{2*7}=\frac{-84}{14}
=-6
$