7x=6x^2-5

Solution for 7x=6x^2-5 equation:

7x=6x^2-5

We move all terms to the left:

7x-(6x^2-5)=0

We get rid of parentheses

-6x^2+7x+5=0

a = -6; b = 7; c = +5;
Δ = b2-4ac
Δ = 72-4·(-6)·5
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*-6}=\frac{-20}{-12}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*-6}=\frac{6}{-12}
=-1/2
$