(8x+7)+(6x+14)=x2

Solution for (8x+7)+(6x+14)=x2 equation:

(8x+7)+(6x+14)=x2

We move all terms to the left:

(8x+7)+(6x+14)-(x2)=0

We add all the numbers together, and all the variables

-1x^2+(8x+7)+(6x+14)=0

We get rid of parentheses

-1x^2+8x+6x+7+14=0

We add all the numbers together, and all the variables

-1x^2+14x+21=0

a = -1; b = 14; c = +21;
Δ = b2-4ac
Δ = 142-4·(-1)·21
Δ = 280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{70}}{2*-1}=\frac{-14-2\sqrt{70}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{70}}{2*-1}=\frac{-14+2\sqrt{70}}{-2}
$