5x^2+7x=12

Solution for 5x^2+7x=12 equation:

5x^2+7x=12

We move all terms to the left:

5x^2+7x-(12)=0

a = 5; b = 7; c = -12;
Δ = b2-4ac
Δ = 72-4·5·(-12)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-17}{2*5}=\frac{-24}{10}
=-2+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+17}{2*5}=\frac{10}{10}
=1
$