10x^2+37x=-7

Solution for 10x^2+37x=-7 equation:

10x^2+37x=-7

We move all terms to the left:

10x^2+37x-(-7)=0

We add all the numbers together, and all the variables

10x^2+37x+7=0

a = 10; b = 37; c = +7;
Δ = b2-4ac
Δ = 372-4·10·7
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-33}{2*10}=\frac{-70}{20}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+33}{2*10}=\frac{-4}{20}
=-1/5
$