2x(6x-7)+(103-x)=180

Solution for 2x(6x-7)+(103-x)=180 equation:

2x(6x-7)+(103-x)=180

We move all terms to the left:

2x(6x-7)+(103-x)-(180)=0

We add all the numbers together, and all the variables

2x(6x-7)+(-1x+103)-180=0

We multiply parentheses

12x^2-14x+(-1x+103)-180=0

We get rid of parentheses

12x^2-14x-1x+103-180=0

We add all the numbers together, and all the variables

12x^2-15x-77=0

a = 12; b = -15; c = -77;
Δ = b2-4ac
Δ = -152-4·12·(-77)
Δ = 3921
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{-(-15)-\sqrt{3921}}{2*12}=\frac{15-\sqrt{3921}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{3921}}{2*12}=\frac{15+\sqrt{3921}}{24}
$