2x(x+30)+(x+10)=1375

Solution for 2x(x+30)+(x+10)=1375 equation:

2x(x+30)+(x+10)=1375

We move all terms to the left:

2x(x+30)+(x+10)-(1375)=0

We multiply parentheses

2x^2+60x+(x+10)-1375=0

We get rid of parentheses

2x^2+60x+x+10-1375=0

We add all the numbers together, and all the variables

2x^2+61x-1365=0

a = 2; b = 61; c = -1365;
Δ = b2-4ac
Δ = 612-4·2·(-1365)
Δ = 14641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14641}=121$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-121}{2*2}=\frac{-182}{4}
=-45+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+121}{2*2}=\frac{60}{4}
=15
$