7x^2+12x=152

Solution for 7x^2+12x=152 equation:

7x^2+12x=152

We move all terms to the left:

7x^2+12x-(152)=0

a = 7; b = 12; c = -152;
Δ = b2-4ac
Δ = 122-4·7·(-152)
Δ = 4400
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:

$\sqrt{\Delta}=\sqrt{4400}=\sqrt{400*11}=\sqrt{400}*\sqrt{11}=20\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-20\sqrt{11}}{2*7}=\frac{-12-20\sqrt{11}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+20\sqrt{11}}{2*7}=\frac{-12+20\sqrt{11}}{14}
$