7x(7x+1)+(8x+3)=180

Solution for 7x(7x+1)+(8x+3)=180 equation:

7x(7x+1)+(8x+3)=180

We move all terms to the left:

7x(7x+1)+(8x+3)-(180)=0

We multiply parentheses

49x^2+7x+(8x+3)-180=0

We get rid of parentheses

49x^2+7x+8x+3-180=0

We add all the numbers together, and all the variables

49x^2+15x-177=0

a = 49; b = 15; c = -177;
Δ = b2-4ac
Δ = 152-4·49·(-177)
Δ = 34917
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{34917}}{2*49}=\frac{-15-\sqrt{34917}}{98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{34917}}{2*49}=\frac{-15+\sqrt{34917}}{98}
$