(7x+24)(7x-26)=180

Solution for (7x+24)(7x-26)=180 equation:

(7x+24)(7x-26)=180

We move all terms to the left:

(7x+24)(7x-26)-(180)=0

We multiply parentheses ..

(+49x^2-182x+168x-624)-180=0

We get rid of parentheses

49x^2-182x+168x-624-180=0

We add all the numbers together, and all the variables

49x^2-14x-804=0

a = 49; b = -14; c = -804;
Δ = b2-4ac
Δ = -142-4·49·(-804)
Δ = 157780
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:

$\sqrt{\Delta}=\sqrt{157780}=\sqrt{196*805}=\sqrt{196}*\sqrt{805}=14\sqrt{805}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14\sqrt{805}}{2*49}=\frac{14-14\sqrt{805}}{98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14\sqrt{805}}{2*49}=\frac{14+14\sqrt{805}}{98}
$