25x^2+10x-6=7

Solution for 25x^2+10x-6=7 equation:

25x^2+10x-6=7

We move all terms to the left:

25x^2+10x-6-(7)=0

We add all the numbers together, and all the variables

25x^2+10x-13=0

a = 25; b = 10; c = -13;
Δ = b2-4ac
Δ = 102-4·25·(-13)
Δ = 1400
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:

$\sqrt{\Delta}=\sqrt{1400}=\sqrt{100*14}=\sqrt{100}*\sqrt{14}=10\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{14}}{2*25}=\frac{-10-10\sqrt{14}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{14}}{2*25}=\frac{-10+10\sqrt{14}}{50}
$