7x^2-21x+110=180

Solution for 7x^2-21x+110=180 equation:

7x^2-21x+110=180

We move all terms to the left:

7x^2-21x+110-(180)=0

We add all the numbers together, and all the variables

7x^2-21x-70=0

a = 7; b = -21; c = -70;
Δ = b2-4ac
Δ = -212-4·7·(-70)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-49}{2*7}=\frac{-28}{14}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+49}{2*7}=\frac{70}{14}
=5
$