(3x+1)(2x-1)=1150

Solution for (3x+1)(2x-1)=1150 equation:

(3x+1)(2x-1)=1150

We move all terms to the left:

(3x+1)(2x-1)-(1150)=0

We multiply parentheses ..

(+6x^2-3x+2x-1)-1150=0

We get rid of parentheses

6x^2-3x+2x-1-1150=0

We add all the numbers together, and all the variables

6x^2-1x-1151=0

a = 6; b = -1; c = -1151;
Δ = b2-4ac
Δ = -12-4·6·(-1151)
Δ = 27625
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:

$\sqrt{\Delta}=\sqrt{27625}=\sqrt{25*1105}=\sqrt{25}*\sqrt{1105}=5\sqrt{1105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5\sqrt{1105}}{2*6}=\frac{1-5\sqrt{1105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5\sqrt{1105}}{2*6}=\frac{1+5\sqrt{1105}}{12}
$