x(3x-10)+70=180

Solution for x(3x-10)+70=180 equation:

x(3x-10)+70=180

We move all terms to the left:

x(3x-10)+70-(180)=0

We add all the numbers together, and all the variables

x(3x-10)-110=0

We multiply parentheses

3x^2-10x-110=0

a = 3; b = -10; c = -110;
Δ = b2-4ac
Δ = -102-4·3·(-110)
Δ = 1420
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:

$\sqrt{\Delta}=\sqrt{1420}=\sqrt{4*355}=\sqrt{4}*\sqrt{355}=2\sqrt{355}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{355}}{2*3}=\frac{10-2\sqrt{355}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{355}}{2*3}=\frac{10+2\sqrt{355}}{6}
$