6x2-13x-7=+x2+x-5

Solution for 6x2-13x-7=+x2+x-5 equation:

6x^2-13x-7=+x2+x-5

We move all terms to the left:

6x^2-13x-7-(+x2+x-5)=0

We add all the numbers together, and all the variables

6x^2-(+x^2+x-5)-13x-7=0

We get rid of parentheses

6x^2-x^2-x-13x+5-7=0

We add all the numbers together, and all the variables

5x^2-14x-2=0

a = 5; b = -14; c = -2;
Δ = b2-4ac
Δ = -142-4·5·(-2)
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{59}}{2*5}=\frac{14-2\sqrt{59}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{59}}{2*5}=\frac{14+2\sqrt{59}}{10}
$